Step 1

Let matrix A and B as:

\(A=\begin{bmatrix}2 & 3 \\5& 1 \end{bmatrix}\)

\(B=\begin{bmatrix}1 & 2 \\0 & 1 \end{bmatrix}\) Step 2 The summation of matrices:

\(A+B=\begin{bmatrix}2 & 3 \\5& 1 \end{bmatrix}+ \begin{bmatrix}1 & 2 \\0 & 1 \end{bmatrix}\)

\(A+B=\begin{bmatrix}3 & 5 \\5 & 2 \end{bmatrix}\)

Step 3

Determinant of summation of matrices:

\(|A+B|=3(2)-5(5)=6-25=-19\)

Step 4

Determinant of matrix A and matrix B

\(|A|=\begin{bmatrix}2 & 3 \\5& 1 \end{bmatrix}=2(1)-3(5)=2-15=-13\)

\(|B|=\begin{bmatrix}1 & 2 \\0 & 1 \end{bmatrix}=1(1)-2(0)=1-0=1\)

Step 5

Hence, it is clear that:

\(|A+B|\neq |A|+|B|\)