Given : and

Matrix A is of order 3 2, and Matrix B is of order 2 2

To find : matrix AB and 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 = 3,b = c = 2,d = 2 ,thus matrix AB is of order 3 2

Matrix AB =

Matrix AB =

Matrix AB =

Matrix AB =

For matrix BA, a = 3,b = c = 2,d = 2 ,thus matrix BA exists, if and only if d=a

But 3 2

Thus matrix BA does not exist