Find the inverse the matrix (if it exists)given in`[(1,-1, 2),( 0, 2,-3),( 3,-2, 4)]`

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{pmatrix} \), we will follow these steps:

### Step 1: Calculate the Determinant of the Matrix
The determinant of a 3x3 matrix \( A = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} \) is given by the formula:
\[ \text{det}(A) = a(ei - fh) - b(di - fg) + c(dh - eg) \]
For our matrix:
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