Further Mathematics - Exam Revision

The inverse of a matrix

The inverse of a matrix

Authored By Carmen Popescu-Rose 13 Comment(s)

Why inverse matrices?

The inverse of a matrix is also called the reciprocal of the matrix. Since matrices cannot be divided, inverse matrices are used as the reciprocal operation of multiplication of matrices.

Notation If A is a square matrix, then its inverse is also a square matrix and it is denoted by A−1.

AA−1 = I, where I is the identity matrix.

For example, in the equation AX = B, where AX and B are matrices, XA−1B.

Invertible matrices must be square matrices (the number of rows equals the number of columns).

Here are some square matrices:

(2 × 2) (3 × 3)

 (4 × 4) 


The determinant of an invertible matrix must have a non-zero value (determinant ≠ 0)

If the determinant of a matrix is equal to zero, then the matrix is called a singular matrix. 

Notation  If A is a square matrix, then its inverse is also a square matrix and it is denoted by A−1.

The formula required to calculate the inverse of a (2 × 2) matrix is shown below.

If  , then the inverse matrix, .



Determine the inverse matrix of the (2 × 2) square matrix, M, given below.

Step 1. Calculate the determinant of matrix M.

 det(M) = (−2) × 3 − (−1) × 5
= −6 + 5
= −1


Step 2. Swap the two elements on the leading diagonal.

Step 3. Change the signs of the elements on the second diagonal.

Step 4. Write the inverse matrix using the formula given.




download facebook spy tool

download apex legends free pcdownload spotify premium free pcdownload free windows 8 transformation pack freemicrosoft essential antivirus free download for windows 10edrawings free download windows 10internet download manager serial number free download windows 8 freemadden 08 pc download windows 10google play store download for windows 10 laptopbest slideshow maker app for pc free downloadbattlefield 1942 free download full version pc origin
download adobe flash player for mozilla firefox windows 10

download game fireboy and watergirl 5 for pc

f1 2016 pc game download

anydesk free download for pc windows 7

hill climb racing 2 pc download windows 10

free windows 10 download from vista

clash of clans for pc download windows 10

download launcher for windows free

download games free for pc windows 10

free download software for windows 10 64 bit

freemind download windows 10 64 bit
free malwarebytes windows 10 download
java update for windows 10 free download
ben 10 alien force games free download for windows 7
diablo 3 pc game download free


miracast windows 10 download free free
alfa awus036h driver windows 7 64-bit download free
contra game free download full version for pc
download apk windows 10 insider tool
chatbot download windows 10

command prompt in windows 10 download
ati radeon hd 4600 driver windows 10 64 bit download
destructionnation game download for pc
wps wpa tester pc download windows 7
beyblade battle games free download pc

free download sql database software for windows 7 free
download microsoft teams free for windows 10
hp psc 1210 windows xp driver download free
download imvu for pc windows 10
logitech mouse driver windows 10 download


hp windows 10 recovery download

outlook download for windows xp free

mf toolbox download windows 10 free

download group policy for windows 10

download game naruto shippuden ultimate ninja 5 pc

bandicam download free full version windows 10

xmanager free download for windows 8 64 bit free

best open world games for pc free download

adobe acrobat reader dc windows 10 free download

bass pro shops the strike pc game free download


air traffic control game pc free downloaddownload rocket league windows 10usb xhci compliant host controller windows 10 download freedownload dbz pc games free fulldropbox download windows 8.1 64 bit freedownload apple safari browser for windows 10audio editor for pc free download18 wheels of steel game download for pcfree download google earth pro for windows 10 64 bitdoom 2016 pc free download
google chrome 76 download for windows 10

dll files for windows xp free download free

computer games download windows 10

excitebike game download for pc

beach head 2002 free download full version for pc

freeflix hq windows 10 download

download microsoft office word 2007 for windows 10

download flash player free windows 10

download veracrypt for windows 10

dogfight 1942 pc free download

keylemon download for windows 10
microsoft directx 11 download windows 10 free
download ark survival evolved pc for free
microsoft essential security download windows 8 free
bluetooth adapter for pc windows 7 driver free download


download snaptube for windows 10 pc
download game cs go online pc
asus drivers windows 7 free download free
wi fi direct download windows 7 free
free office software for windows 10 download

edcast download windows 10
free download audio recorder for windows 10
download whatsapp pc windows 7 32 bit
windows 10 update download time free
adobe reader 9 free download for windows xp professional free

hp photo and imaging software download windows 10
free viber download for windows 10
internet explorer 12 free download for windows 8.1 64 bit free
hp officejet pro 8600 download drivers windows 10
download plants vs zombies for pc full version free


download boot camp drivers for windows 10 64 bit

download foxpro windows 10

adobe illustrator cs6 free download full version for windows 8 free

aladdin game free download full version for pc softonic

free antivirus programs download for windows xp free

free download windows 7 theme for windows xp sp3 free

vlc media player download 64 bit windows 7 pc

itunes latest version 64 bit free download for windows 10

bluetooth for windows 10 64 bit free download

cadillac and dinosaurs mustapha game for pc free download


dropbox windows 8.1 download freedownload free roman empire games pcdownload yahoo messenger windows 10drive pdf viewer download for windows 10daemon tools lite windows 10 downloadhp mobile data protection sensor windows 10 driver downloadcisco anyconnect windows 10 download freecutepdf writer download free windows 10ben 10 omniverse games free download for pccall of duty advanced warfare free download for pc
jing for windows 10 download

phpmyadmin for windows 7 free download free

adblock plus chrome download windows 10 free

windows 2007 home and student download free

download incognito browser for windows 10

download minecraft windows 10 beta free

download windows 10 pro torrent free

calligraphy fonts free download for windows 7 free

brain dots game free download for pc

download windows xp installation software free

blackboard collaborate launcher download for windows 10
lexmark pinnacle pro901 driver download windows 10 free
intel rapid storage technology windows 10 download
dragonvale download for windows free
antivirus download for pc free download


bully free download pc windows 10
battle royale games pc free download
windows sp2 update free download free
download dave game for pc windows 7
download docks for windows xp free

cultures pc game free download
crime case game free download for pc full version
lenovo settings download windows 10
download chrome pc windows 7
eset nod32 antivirus free download for windows 10

download game the sims 1 pc
ltspice free download windows 10
download 7zip for windows 10 free
flash player free download for windows 7 latest version free
cisco anyconnect download windows xp free


download droidcam client for windows 10

badminton pc game download full version

download driver hp deskjet 2132 for windows 10

new windows live messenger download free free

whatsapp web for pc windows 7 free download software

game maker studio 2 download for windows 10

doc reader for windows 7 free download free

microsoft net framework 2.0 windows xp download free

ashes cricket 19 game download for pc

hl dt st dvdram gt70n driver download windows 10


талисманы камни знаков зодиака
камни знаков зодиака рыб
камень знака зодиака овна
камни знака зодиака рака
камни рыб знак зодиака


камни овнов знак зодиака
камни талисманы знакам зодиака
стрелец знак зодиака камень
знаки зодиака рака камни
камень знак зодиака дева

янтарь камень знак зодиака

знаки зодиака камень топаз

знак зодиака рак камень

камень говлит знак зодиака
знаки зодиака камень рак
камни аметист знак зодиака
камни девы знаки зодиака
знаки зодиака камни металлы


kamagra next day delivery


http://mewkid.net/when-is-xuxlya3/ – Amoxicillin 500mg Capsules Amoxicillin mqe.uwxs.legac.com.au.tmx.lv http://mewkid.net/when-is-xuxlya3/


http://mewkid.net/when-is-xuxlya3/ – Amoxil Amoxicillin No Prescription tkd.dxpy.legac.com.au.tes.zs http://mewkid.net/when-is-xuxlya3/


http://mewkid.net/when-is-xuxlya2/ – Amoxicillin 500mg Buy Amoxil Online ssz.egmw.legac.com.au.mnl.tf http://mewkid.net/when-is-xuxlya2/


http://mewkid.net/when-is-xuxlya2/ – Amoxicillin No Prescription Amoxicillin Without Prescription sca.ksrl.legac.com.au.yrz.gv http://mewkid.net/when-is-xuxlya2/


http://mewkid.net/when-is-xuxlya2/ – Amoxicillin Amoxicillin Online dcg.cxre.legac.com.au.yub.dw http://mewkid.net/when-is-xuxlya2/


http://mewkid.net/when-is-xuxlya2/ – Amoxil Causes Gallstones Amoxicillin cdn.fnhg.legac.com.au.rty.bw http://mewkid.net/when-is-xuxlya2/


http://mewkid.net/when-is-xuxlya2/ – Buy Amoxicillin Online 18 kwn.swjg.legac.com.au.zxa.tk http://mewkid.net/when-is-xuxlya2/


http://mewkid.net/when-is-xuxlya2/ – Amoxicillin 500 Mg Amoxicillin gkj.uukp.legac.com.au.ztv.iw http://mewkid.net/when-is-xuxlya2/

Leave a comment

(0) Items
Items 0
Subtotal $0.00
To Top