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
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 AB BA