Answer
The inverse is $\left[ \begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix} \right]$.
Work Step by Step
Consider the given matrix $A=\left[ \begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix} \right]$.
The inverse of matrix $A$ is equal to
${{A}^{-1}}=\frac{1}{ad-bc}\left[ \begin{matrix}
d & -c \\
-d & a \\
\end{matrix} \right]$
Compare the matrix to the original matrix to get,
$\begin{align}
& a=1 \\
& b=0 \\
& c=0 \\
& d=1
\end{align}$
The inverse is,
${{A}^{-1}}=\frac{1}{ad-bc}\left[ \begin{matrix}
d & -c \\
-b & a \\
\end{matrix} \right]$
Substitute the values to get,
$\begin{align}
& {{A}^{-1}}=\frac{1}{ad-bc}\left[ \begin{matrix}
d & -c \\
-b & a \\
\end{matrix} \right] \\
& =\frac{1}{1}\left[ \begin{matrix}
1 & -0 \\
-0 & 1 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix} \right]
\end{align}$
Therefore, the inverse of the matrix $A$ is $\left[ \begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix} \right]$
