If `A=[(k,l),(m,n)]` and `kn!=lm,` show that `A^(2)-(k+n)A+(kn-lm)l=O.` Hence, find `A^(-1)`

Explanation

To solve the problem, we need to show that \( A^2 - (k+n)A + (kn - lm)I = O \) and then find the inverse of matrix \( A \).

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

Given the matrix \( A = \begin{pmatrix} k & l \\ m & n \end{pmatrix} \), we can calculate \( A^2 \) as follows:

\[
A^2 = A \cdot A = \begin{pmatrix} k & l \\ m & n \end{pmatrix} \cdot \begin{pmatrix} k & l \\ m & n \end{pmatrix}
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