If `A=[[1 ,2,-3],[ 5, 0, 2],[ 1,-1, 1]], B=[[3,-1, 2],[ 4, 2 ,5],[ 2, 0, 3]]`and `C=[[4, 1, 2],[ 0, 3, 2],[ 1,-2, 3]]`, then compute `(A+B)` and `(B - C)`. Also, verify that `A + (B - C) = (A + B) - C`.

Explanation

To solve the problem step by step, we will first compute the matrices \( A + B \) and \( B - C \), and then verify that \( A + (B - C) = (A + B) - C \).

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

Given:
\[ A = \begin{bmatrix} 1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{bmatrix} \]
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