If `A=[[0, 6, 7], [-6, 0, 8], [ 7,-8, 0]]`, `B=[[0, 1, 1],[ 1, 0, 2],[ 1, 2, 0]]`, `C=[[2], [-2] , [3]]`Calculate AC, BC and `(A + B)C`. Also, verify that `(A + B)C = A C + B C`

Explanation

To solve the problem, we will calculate \( AC \), \( BC \), and \( (A + B)C \), and then verify that \( (A + B)C = AC + BC \).

### Step 1: Calculate \( A + B \)

Given:
\[ A = \begin{bmatrix} 0 & 6 & 7 \\ -6 & 0 & 8 \\ 7 & -8 & 0 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 2 \\ 1 & 2 & 0 \end{bmatrix} \]

To find \( A + B \), we add the corresponding elements of matrices \( A \) and \( B \):
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