For the following matrices, verify that A(BC) = (AB)C :

and


Given : and


Matrix A is of order 2 3 , matrix B is of order 3 3 and matrix C is of order 3 1


To show : matrix A(BC) = (AB)C


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 BC, a = 3,b = c = 3,d = 1 ,thus matrix BC is of order 3 1


Matrix BC = = =


Matrix BC =


For matrix A(BC),a = 2 ,b = c = 3 ,d = 1 ,thus matrix A(BC) is of order 2 x 1


Matrix A(BC) = = =


Matrix A(BC) =


Matrix A(BC) =


For matrix AB, a = 2,b = c = 3,d = 3 ,thus matrix BC is of order 2 3


Matrix AB =


Matrix AB =


Matrix AB = =


Matrix AB =


For matrix (AB)C, a = 2,b = c = 3,d = 1 ,thus matrix (AB)C is of order 2 1


Matrix (AB)C = =


Matrix (AB)C = =


Matrix (AB)C =


Matrix A(BC) = (AB)C =


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