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
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
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.

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