Let, A = \(
\begin{bmatrix}
1& 2 \\[0.3em]
2& -1 \\[0.3em]
\end{bmatrix}\)
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 the Identity matrix.
Therefore, we get the A-1 as,
A-1 = \(
\begin{bmatrix}
\frac{1}{5} &\frac{2}{5} \\[0.3em]
\frac{2}{5}&-\frac{1}{5} \\[0.3em]
\end{bmatrix}\)
The value of A-1 is correct or not can be verified by the formula: AA-1 = I