Q. 3 B

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

and

Answer :

Given : and


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


To show : matrix AB BA


Formula used : 3x3-matrix-formula.png


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


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