Answer
$A=\begin{bmatrix}
0& 0 \\
0&0\\
\end{bmatrix}$ and $B= \begin{bmatrix}
1& 0 \\
0&1\\
\end{bmatrix}$
Work Step by Step
Let $A=\begin{bmatrix}
0& 0 \\
0&0\\
\end{bmatrix}$ and $B= \begin{bmatrix}
1& 0 \\
0&1\\
\end{bmatrix}$
then $A+B= \begin{bmatrix}
1& 0 \\
0&1\\
\end{bmatrix}$
We know that for a matrix
$
\left[\begin{array}{rr}
a & b \\
c &d \\
\end{array} \right]
$
the determinant, $D=ad-bc.$
Hence $|A|=0\cdot0-0\cdot0=0-0=0$, $|B|=1\cdot1-0\cdot0=1-0=1$ and $|A+B|=1\cdot1-0\cdot0=1-0=1$, thus $|A|+|B|=|A+B|$.
