Answer
The number 1 is the multiple identity. When the number is multiplied by the digit 1, the number doesn’t change.
Work Step by Step
The multiplicative identity of the matrix is denoted by ${{I}_{N}}$. The $n\times n$ square matrix consists of $n$ elements on the diagonal with the value 1 and 0s elsewhere. The multiplicative identity is the property of multiplication that states: when 1 is multiplied by any real number, the real number does not change; therefore the number 1 is called the multiplicative identity for real numbers.
Consider a matrix, such that,
$\begin{align}
& {{I}_{1}}=\left[ 1 \right] \\
& {{I}_{2}}=\left[ \begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix} \right] \\
& {{I}_{3}}=\left[ \begin{matrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \\
\end{matrix} \right] \\
\end{align}$
These are the examples of identity matrices of order $1\times 1,2\times 2,3\times 3,\ldots ,n\times n.$
Consider, $M=\left[ \begin{matrix}
-4 & -3 \\
-6 & 5 \\
\end{matrix} \right]$
This is a square matrix of order $2\times 2$.
The identity matrix is, $\left[ \begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix} \right]$
Now, the rule of matrix multiplication is $A=MI$
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 $\left[ \begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix} \right]$.
