Let, A = \( \begin{bmatrix} 2 & -3 \\[0.3em] 4& 5 \\[0.3em] \end{bmatrix}\)
Now we are going to write the Augmented Matrix followed by matrix A and the Identity matrix I, i.e.,
Now our job is to convert the matrix A into Identity Matrix.
Therefore, the matrix we will get converting the matrix I will be our A-1.
Here, the matrix A is converted into Identity matrix.
Therefore, we get the A-1 as,
A-1 = \( \begin{bmatrix} \frac{5}{22} & \frac{3}{22} \\[0.3em] -\frac{2}{11} &\frac{1}{11} \\[0.3em] \end{bmatrix}\)
The value of A-1 is correct or not can be verified by the formula: AA-1 = I