For the following matrices verify the associativity of matrix multiplication i.e. (AB) C = A(BC). A=[(1,2,0)(-1,0,1)],

Question

For the following matrices verify the associativity of matrix multiplication i.e. (AB) C = A(BC).

A = \(\begin{bmatrix} 1 &2 & 0 \\[0.3em] -1 & 0 & 1 \end{bmatrix}\), B = \(\begin{bmatrix}1 &0 \\[0.3em] -1 &2 \\[0.3em] 0 & 3 \end{bmatrix}\)and C = \(\begin{bmatrix}1 \\[0.3em] -1 \end{bmatrix}\)

Answer 1

Given, 

A = \(\begin{bmatrix} 1 &2 & 0 \\[0.3em] -1 & 0 & 1 \end{bmatrix}\), 

B = \(\begin{bmatrix}1 &0 \\[0.3em] -1 &2 \\[0.3em] 0 & 3 \end{bmatrix}\)and C = \(\begin{bmatrix}1 \\[0.3em] -1 \end{bmatrix}\)

From equation (1) and (2) we get,

A(BC) = A(BC)