Answer
$AB=BA$ and matrix $B$ shows a multiplicative identity for $2 \times 2$ matrices.
Work Step by Step
We are given that $A=\begin{bmatrix} a & b \\ c & d \end{bmatrix} $ and $B=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $
Now, $AB=\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} =\begin{bmatrix} a & b \\ c & d \end{bmatrix} $
and $BA=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} a & b \\ c & d \end{bmatrix} =\begin{bmatrix} a & b \\ c & d \end{bmatrix} $
This follows that $AB=BA$ and matrix $B$ shows a multiplicative identity for $2 \times 2$ matrices.
