Question

Could someone take a look at these two matrix problem examples to ensure that my understanding is correct?

Answer 1

\[\left[\begin{matrix}1 & 2 \\ 3 & 4\end{matrix}\right] x \left[\begin{matrix}5 & 6 \\ 7 & 8\end{matrix}\right]= \left[\begin{matrix}26 & 46 \\ 78 & 104\end{matrix}\right]\]

Answer 2

My work:
1x5+1x6+1x7+1x8=26
2x5+2x6+2x7+2x8=46
3x5+3x6+3x7+3x8=78
4x5+4x6+4x7+4x8=104

Answer 3

\[2x \left[\begin{matrix}1 & 2 \\ 3 & 4\end{matrix}\right]=\left[\begin{matrix}2 & 4 \\ 6 & 8\end{matrix}\right]\]

Answer 4

Same as example 1, but I multiplied the real (or scalar) number by the numbers within the matrix