Let, A = \( \begin{bmatrix} 1& 2 \\[0.3em] 3& 7 \\[0.3em] \end{bmatrix}\)
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 = \( \begin{bmatrix} 7& -2 \\[0.3em] -3& 1 \\[0.3em] \end{bmatrix}\)
The value of A -1 is correct or not can be verified by the formula: AA-1 = I