Dear student,

We have to verify that (AB)C = A(BC).

Now firstly we perform (AB). A is a 1*3 matrix, B is a 3*2 matrix and C is a 2*2 matrix.

now AB = [17  32] i.e. a 1*2 matrix

now (AB)C = [230  273] i.e a 1*2 matrix

On the other hand we have :

BC = [ 0/16/66  -22/32/77] i.e. a 3*2 matrix

now A(BC) = [ 230   273]

Now clearly we see that (AB)C = A(BC)

Hence we can say that matrices multiplication follows the associative law.

Hope it helps.