If `A=[[3, 1],[-1, 2]]`
, show that `A^2-5A+7I=O`
. Hence, find `A^(-1)`
.
Text Solution
AI Generated Solution
To solve the problem, we need to show that \( A^2 - 5A + 7I = O \) for the matrix \( A = \begin{pmatrix} 3 & 1 \\ -1 & 2 \end{pmatrix} \), and then find the inverse of \( A \).
### Step 1: Calculate \( A^2 \)
First, we need to compute \( A^2 \):
\[
A^2 = A \cdot A = \begin{pmatrix} 3 & 1 \\ -1 & 2 \end{pmatrix} \cdot \begin{pmatrix} 3 & 1 \\ -1 & 2 \end{pmatrix}
...
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