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 c_ij = a_i1b_1j + a_i2b_2j + a_i3b_3j + ……………… + a_inb_nj

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 =