Answer
$\left[\begin{array}{rrr}
9 & 4 & -5\\
0 & -6 & -15\\
1 & 0 & -5
\end{array}\right]$
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.
$AB=\left[\begin{array}{lll}
1(1)+2(4)+0(0) & 1(2)+2(1)+0(-2) & 1(-4)+0(0)-1(1)\\
4(1)-1(4)+1(0) & 4(2)-12(1)+1(-2) & 4(-4)-1(0)+1(1)\\
1(1)+0(4)+1(0) & 1(2)+0(1)+1(-2) & 1(-4)+0(0)-1(1)
\end{array}\right]$
$=\left[\begin{array}{lll}
9 & 4 & -5\\
0 & -6 & -15\\
1 & 0 & -5
\end{array}\right]$
