Find the inverse the matrix (if it exists)given in`[(1, 0, 0),( 0,cosalpha ,sinalpha),(0, sinalpha, -cosalpha)]`

Explanation

To find the inverse of the given matrix \( A = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos \alpha & \sin \alpha \\ 0 & \sin \alpha & -\cos \alpha \end{pmatrix} \), we will follow these steps:

### Step 1: Calculate the Determinant of the Matrix
To find the inverse, we first need to check if the determinant of the matrix \( A \) is non-zero.

\[ \text{det}(A) = 1 \cdot \begin{vmatrix} \cos \alpha & \sin \alpha \\ \sin \alpha & -\cos \alpha \end{vmatrix} \]
...