If `A=[(2, 0, 1 ),(2, 1, 3),( 1,-1, 0)]` , find `A^2-5A+4I` and hence find a matrix `X` such that `A^2-5A+4I+X=O` .

Explanation

To solve the problem, we need to calculate \( A^2 - 5A + 4I \) where \( A = \begin{pmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{pmatrix} \) and \( I \) is the identity matrix of the same order as \( A \).

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

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

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