Find the characteristic equation of the matrix` A= [(2,1),(3,2)]` and hence find its inverse using Cayley-hamilton theorem.

Explanation

To find the characteristic equation of the matrix \( A = \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix} \) and then use the Cayley-Hamilton theorem to find its inverse, we will follow these steps:

### Step 1: Find the Characteristic Polynomial
The characteristic polynomial of a matrix \( A \) is given by the determinant of \( A - \lambda I \), where \( I \) is the identity matrix and \( \lambda \) is a scalar.

1. **Set up the matrix \( A - \lambda I \):**
\[
A - \lambda I = \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix} - \begin{pmatrix} \lambda & 0 \\ 0 & \lambda \end{pmatrix} = \begin{pmatrix} 2 - \lambda & 1 \\ 3 & 2 - \lambda \end{pmatrix}
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