If `A=[[1, 0],[ 0,-1]]`and `B=[[0 ,1], [1, 0]]`, then find AB,BA. Show that 'A B!=B A`.

Explanation

To solve the problem, we need to find the products of the matrices \( AB \) and \( BA \) and then show that \( AB \neq BA \).

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

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