If `A=[[1,0],[ 0,-1]]`and `B=[[0, 1],[ 1 ,0]]`, then `A B=[[0,1],[-1, 0]]`and `B A=[[0,-1],[ 1, 0]]`. Clearly `A B!=B A`.

Explanation

To solve the problem, we need to compute the products of the matrices \( A \) and \( B \) in both orders, \( AB \) and \( BA \), and then compare the results.

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

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