Show that AB ≠ BA in each of the following cases :

and

Given : and

Matrix A is of order 3 3, and Matrix B is of order 3 3

To show : matrix AB BA

The 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 =

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 = and Matrix AB =

Matrix AB BA