Q. 6 B4.2( 5 Votes )

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

and C = [1 -2]

Answer :

Given : and C = [1 -2]


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


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 = 1,d = 2 ,thus matrix BC is of order 3 2


Matrix BC = = =


Matrix BC =


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


Matrix A(BC) = =


Matrix A(BC) = =


Matrix A(BC) =


Matrix A(BC) =


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


Matrix AB = =


Matrix AB = =


Matrix AB =


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


Matrix (AB)C = = =


Matrix (AB)C =


Matrix A(BC) = (AB)C =


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