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If A={:[(1,2,0),(-1,0,1),(1,2,1)]:},B={:...

If `A={:[(1,2,0),(-1,0,1),(1,2,1)]:},B={:[(1,2),(2,1),(-1,1)]:}andC={:[(1,0,0,1),(1,2,1,2)]:}` Find A(BC), (AB)C and prove that A(BC)=(AB)C.

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To solve the problem, we need to calculate \( A(BC) \) and \( (AB)C \) and then verify that they are equal. Given matrices: \[ A = \begin{pmatrix} 1 & 2 & 0 \\ -1 & 0 & 1 \\ 1 & 2 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & 2 \\ 2 & 1 \\ -1 & 1 \end{pmatrix}, \quad C = \begin{pmatrix} 1 & 0 & 0 & 1 \\ 1 & 2 & 1 & 2 \end{pmatrix} \] ### Step 1: Calculate \( BC \) ...
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