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