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

and

Given : and

Matrix A is of order 2 2 and Matrix B is of order 2 2

To show : matrix AB = BA

Formula used :

Where c_ij = a_i1b_1j + a_i2b_2j + a_i3b_3j + ……………… + a_inb_nj

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 = 2,b = c = 2,d = 2 ,thus matrix AB is of order 2 2

Matrix AB =

Matrix AB =

Matrix AB =

For matrix BA, a = 2,b = c = 2,d = 2 ,thus matrix BA is of order 2 2

Matrix BA=

Matrix BA =

Matrix BA = Matrix AB =

Thus Matrix AB = BA