If `A=[3-2 4-2]` , find the value of `lambda` so that `A^2=lambdaA-2Idot` Hence, find `A^(-1)` .

Explanation

To solve the problem step by step, we will first find \( A^2 \) and then determine the value of \( \lambda \) such that \( A^2 = \lambda A - 2I \). Finally, we will find the inverse of matrix \( A \).

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

Given the matrix:
\[ A = \begin{pmatrix} 3 & -2 \\ 4 & -2 \end{pmatrix} \]
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