If 
and 
shown that AB = A and BA = B.
Given : 
and 
Matrix A is of order 3 
3 and Matrix B is of order 3 
3
To show : matrix AB = A, BA = B
Formula used : 
If A is a matrix of order a 
b and B is a matrix of order c 
d ,then matrix AB exists and is of order a 
d ,if and only if b = c
If A is a matrix of order a 
b and B is a matrix of order c 
d ,then matrix BA exists and is of order c 
b ,if and only if d = a
For matrix AB, a = 3,b = c = 3,d = 3 ,thus matrix AB is of order 3 
3
Matrix AB = 
=
Matrix AB = 
= 
Matrix AB = 
= Matrix A
Matrix AB = Matrix A
For matrix BA, a = 3,b = c = 3,d = 3 ,thus matrix AB is of order 3 
3
Matrix BA = 
Matrix BA = 
Matrix BA = 
= 
Matrix BA = 
= Matrix B
Matrix BA = 
= Matrix B
MATRIX AB = A and MATRIX BA = B
1