If `A=[(2, 3),(5,-2)]` be such that `A^(-1)=k\ A` , then find the value of `k` .

Explanation

To solve for the value of \( k \) in the equation \( A^{-1} = kA \) where \( A = \begin{pmatrix} 2 & 3 \\ 5 & -2 \end{pmatrix} \), we will follow these steps:

### Step 1: Calculate the Determinant of Matrix \( A \)

The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is calculated using the formula:

\[
\text{det}(A) = ad - bc
...