Answer
$\left[\begin{array}{rrr}
1 & -5 & 3\\
0 & 0 & 9\\
0 & 4 & 1
\end{array}\right]$
Work Step by Step
If $A$ is an $m\times\boxed{n }$ matrix and $B$ is an $\boxed{n }\times k$ matrix,
then the product $AB$ is the $m\times k$ matrix whose $ij-$th entry is the product
$(AB)_{ij}=[a_{i1}\ a_{i2}\ a_{i3}\ \ldots\ a_{in}]\left[\begin{array}{l}
b_{1j}\\
b_{2j}\\
b_{3j}\\
\vdots\\
b_{nj}
\end{array}\right]$
$=a_{i1}b_{1j}+a_{i2}b_{2j}+a_{i3}b_{3j}+\cdots+a_{in}b_{nj}$.
-------
Here,
A is a $2\times 2$ matrix, B is a $2\times 2$ matrix
AB is defined, and is a $2\times 2$ matrix.
$AB=\left[\begin{array}{lll}
1(1)+0(1)-1(0) & 1(-1)+0(1)-1(4) & 1(4)+0(0)-1(1)\\
2(1)-2(1)+1(0) & 2(-1)-2(1)+1(4) & 2(4)-2(0)+1(1)\\
0(1)+0(1)+1(0) & 0(-1)+0(1)+1(4) & 0(4)+0(0)+1(1)
\end{array}\right]$
$=\left[\begin{array}{lll}
1 & -5 & 3\\
0 & 0 & 9\\
0 & 4 & 1
\end{array}\right]$