Q. 3 A4.1( 7 Votes )

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

and

Answer :

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 cij = ai1b1j + ai2b2j + ai3b3j + ……………… + ainbnj


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


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