Answer
True, only square matrices have multiplicative inverses.
Work Step by Step
The multiplicative identity of the matrix is denoted by ${{I}_{N}}$. In the $n\times n$ identity square matrix, we have 1s on the diagonal and 0s elsewhere.
The representing of the square identity matrix is given by:
$\begin{align}
& {{I}_{1}}=\left[ 1 \right] \\
& {{I}_{2}}=\left[ \begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix} \right] \\
& {{I}_{3}}=\left[ \begin{matrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \\
\end{matrix} \right] \\
\end{align}$
As example:
Let, $M=\left[ \begin{matrix}
-4 & -3 \\
-6 & 5 \\
\end{matrix} \right]$
This is a square matrix of order $2\times 2$.
And the identity matrix is: $\left[ \begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix} \right]$
Now, the rule of matrix multiplication is given by $A=MI$
Then,
$\begin{align}
& A=\left[ \begin{matrix}
-4 & -3 \\
-6 & 5 \\
\end{matrix} \right]\times \left[ \begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-4 & -3 \\
-6 & 5 \\
\end{matrix} \right]
\end{align}$
Hence, the identity matrix is $A=\left[ \begin{matrix}
-4 & -3 \\
-6 & 5 \\
\end{matrix} \right]$.
