Understanding Engineering Mathematics

[− 123

011

− 102

][ 2 − 4 − 1

− 111

1 − 2 − 1

]

=

[− 100

0 − 10

00 − 1

]

=−

[ 100

010

001

]

=−I

whereIis called the 3× 3 unit matrix. It follows that if

A=

[

− 123

011

− 102

]

and

B=

[− 241

1 − 1 − 1

− 121

]

(note the overall change of sign) then

AB=I

You can also check that

BA=I

We say in these circumstances thatBis theinverseofA– and then of courseAis the
inverse ofB. We will see how to find the inverse matrix in Section 13.6.

Problem 13.7

Evaluate

[

1 − 1

00

][

12

12

]

The product is the 2×2 zero matrix

[

00

00

]

This is an example ofAB= 0 even though neitherAnorBis zero.

Exercises on 13.3

1. If

[

x+y 3

− 1 x−y

]

=

[

2 X+Y

Y−X 1

]

findx,y,X,Y.