If `A=[{:(1,2),(4,1):}]` , then find `A^(2)+2A+7I`.

Explanation

To solve the problem, we need to find \( A^2 + 2A + 7I \) where \( A = \begin{pmatrix} 1 & 2 \\ 4 & 1 \end{pmatrix} \) and \( I \) is the identity matrix of the same order.

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

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

\[
A^2 = A \times A = \begin{pmatrix} 1 & 2 \\ 4 & 1 \end{pmatrix} \times \begin{pmatrix} 1 & 2 \\ 4 & 1 \end{pmatrix}
...