Mathematics 9 (Complete Solutions)

# Q5 Determine whether the given matrices are multiplicative inverses of each other.

(i)

 3 5 4 7

and

 3 5 4 7

(ii)

 1 2 2 3

and

 -3 2 2 -1

Solution:

(i)

 3 5 4 7

and

 7 -5 -4 3

We will find multiplicative inverse of

 3 5 4 7

Let     A =

 3 5 4 7

A-1 =
 Adj A | A |
First we will find | A |
| A | =
 3 5 4 7
| A | = 3(7) - 5(4)
| A | = 21 - 20
| A | = 1
So now we will find Adj A

 7 -5 -4 3

A-1 =

 7 -5 -4 3

1
A-1 =

 7 -5 -4 3

Hence determined that the given matrices are multiplicative inverse of each other.

(ii)

 1 2 2 3

and

 -3 2 2 -1

We will find multiplicative inverse of

 1 2 2 3

Let     A =

 1 2 2 3

A-1 =
 Adj A | A |
First we will find | A |
| A | =
 1 2 2 3
| A | = 1(3) - 2(2)
| A | = 3 - 4
| A | = -1
So now we will find Adj A

 3 -2 -2 1

A-1 =

 3 -2 -2 1

-1
A-1 = -1

 3 -2 -2 1

A-1 =

 3(-1) -2(-1) -2(-1) 1(-1)

A-1 =

 -3 2 2 -1

Hence determined that the given matrices are multiplicative inverse of each other.