For example, let
A =
2
3
1
2






and B = 
2
3
1
2
−




−

be two matrices Now
AB =
2
3
2
3
1
2
1
2
−

 


 

−

 

=
4
3
6
6
1
0
I
2
2
3
4
0
1
−
− +




=
=




−
− +




Also
BA =
1
0
I
0
1

 =



 Thus B is the inverse of A, in other
words B = A– 1 and A is inverse of B, i e