If `A=[{:(1,0,-1),(2,1,3),(0,1, 1):}]` then verify that `A^(2)+A=A(A+I)` , where I is `3xx3` unit matrix.

Explanation

To verify the equation \( A^2 + A = A(A + I) \), where \( A = \begin{pmatrix} 1 & 0 & -1 \\ 2 & 1 & 3 \\ 0 & 1 & 1 \end{pmatrix} \) and \( I \) is the \( 3 \times 3 \) identity matrix, we will follow these steps:

### Step 1: Calculate \( A^2 \)

To find \( A^2 \), we need to multiply matrix \( A \) by itself:

\[
A^2 = A \times A = \begin{pmatrix} 1 & 0 & -1 \\ 2 & 1 & 3 \\ 0 & 1 & 1 \end{pmatrix} \times \begin{pmatrix} 1 & 0 & -1 \\ 2 & 1 & 3 \\ 0 & 1 & 1 \end{pmatrix}
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