A=[ 
3
2
​
  
7
5
​
 ]
∣A∣= 
∣
∣
​
  
3
2
​
  
7
5
​
  
∣
∣
​
 =1

=0
 A 
−1
 = 
∣ A∣
1
​
  adj. A
A 
−1
 =[ 
5
−2
​
  
−7
3
​
 ]
​
 
Again,
​
  
B=[ 
6
7
​
  
8
9
​
 ]
∣B∣= 
∣
∣
​
  
6
7
​
  
8
9
​
  
∣
∣
​
 =−2

=0
B 
−1
 = 
−2
1
​
 [ 
9
−7
​
  
−8
6
​
 ]
​
 
Now Multiply A and B,
AB=[ 
3
2
​
  
7
5
​
 ][ 
6
7
​
  
8
9
​
 ]=[ 
67
47
​
  
87
61
​
 ]
Find determinant of AB :
∣AB∣= 
∣
∣
​
  
67
47
​
  
87
61
​
  
∣
∣
​
 =4087−4089=−2

=0
Now, Verify (AB) 
−1
 =B 
−1
 A 
−1
 
LHS:
∣AB∣= 
∣
∣
​
  
67
47
​
  
87
61
​
  
∣
∣
​
 =4087−4089=−2

=0
and
(AB) 
−1
 = 
−2
1
​
 [ 
61
−47
​
  
−87
67
​
 ]
RHS:
​
  
B 
−1
  A 
−1
 = 
−2
1
​
 [ 
9
−7
​
  
−8
6
​
 ][ 
5
−2
​
  
−7
3
​
 ]
= 
−2
1
​
 [ 
61
−47
​
  
−87
67
​
 ]
​
 
This implies, LHS = RHS (Verified)
