Answer
$\begin{bmatrix}
50&-3\\
18&21
\end{bmatrix}$
Work Step by Step
To Find: (A+B)C
$\textbf{I}: A+B$
We add two matrices by adding their respective individual elements.
$\begin{bmatrix}
0&3&-5\\
1&2&6
\end{bmatrix}+\begin{bmatrix}
4&1&0\\
-2&3&-2
\end{bmatrix} = \begin{bmatrix}
4&4&-5\\
-1&5&4
\end{bmatrix} = M$
$\textbf{II}: MC$
$\begin{bmatrix}
4&4&-5\\
-1&5&4
\end{bmatrix}\times\begin{bmatrix}
4&1\\
6&2\\
-2&3
\end{bmatrix}$
Let the resultant matrix be $Z$.
$\implies Z_{1,1} = (4)(4)+(4)(6)+(-5)(-2) = 50$
$\implies Z_{1,2} = (4)(1)+(4)(2)+(-5)(3) = -3$
$\implies Z_{2,1} = (-1)(4)+(5)(6)+(4)(-2) = 18$
$\implies Z_{2,2} = (-1)(1)+(5)(2)+(4)(3) = 21$
$\therefore Z = \begin{bmatrix}
50&-3\\
18&21
\end{bmatrix}$
