If `A=[[1, 1,-1],[ 2, 0, 3],[ 3,-1, 2]]`, `B=[[1, 3],[0,2],[-1, 4]]`and `C=[[1,2, 3,-4],[ 2, 0,-2, 1]]`, find A(BC), (AB)C and show that `(A B)C = A(B C)`.

Explanation

To solve the problem, we need to compute the matrices \( A(BC) \), \( (AB)C \), and show that \( (AB)C = A(BC) \).

### Step 1: Calculate \( AB \)

Given:
\[ A = \begin{bmatrix} 1 & 1 & -1 \\ 2 & 0 & 3 \\ 3 & -1 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 3 \\ 0 & 2 \\ -1 & 4 \end{bmatrix} \]
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