Answer
$$AB= \left[\begin{array}{ccc}{4} & {-9} & {8} \\{-6}&{-4}&{5}\ \\ {5} & {0} & {-4}\end{array}\right].$$
Work Step by Step
Let $$
A=\left[\begin{array}{ccc}{1} & {0} & {-2} \\ {-3} & {1} & {1} \\ {2} & {0} & {-1}\end{array}\right], B=\left[\begin{array}{ccc}{2} & {3} & {0} \\ {1} & {-1} & {1} \\ {-1} & {6} & {4}\end{array}\right].
$$
Suppose that $A=\left[\begin{array}{ccc}{a_1} & {a_2} & {a_3} \end{array}\right]$, where $a_1,a_2,a_3$ are the columns of $A$. and $B=\left[\begin{array}{ccc}{b_1} \\ {b_2} \\ {b_3} \end{array}\right]$, where $b_1,b_2,b_3$ are the rows of $B$.
Now, we have
$$AB=\left[\begin{array}{ccc}{a_1} & {a_2} & {a_3} \end{array}\right] \left[\begin{array}{ccc}{b_1} \\ {b_2} \\ {b_3} \end{array}\right]
$$and
$$a_1 b_1= \left[\begin{array}{ccc}{1} \\ {-3} \\ {2} \end{array}\right] \left[\begin{array}{ccc}{2}&{3}&{0}\end{array}\right]=\left[\begin{array}{ccc}{2} & {3} & {0} \\ {-6} & {-9} & {0} \\ {4} & {6} & {0}\end{array}\right]$$
$$a_2 b_2= \left[\begin{array}{ccc}{0} \\ {1} \\ {0} \end{array}\right] \left[\begin{array}{ccc}{1}&{-1}&{1}\end{array}\right]=\left[\begin{array}{ccc}{0} & {0} & {0} \\{1}&{-1}&{1}\ \\ {0} & {0} & {0}\end{array}\right]$$
$$a_3b_3= \left[\begin{array}{ccc}{-2} \\ {1} \\ {-1} \end{array}\right] \left[\begin{array}{ccc}{-1}&{6}&{4}\end{array}\right]=\left[\begin{array}{ccc}{2} & {-12} & {-8} \\{-1}&{6}&{4}\ \\ {1} & {-6} & {-4}\end{array}\right].$$
Then,
$$AB=a_1b_1+a_2b_2+a_3b_3=\left[\begin{array}{ccc}{4} & {-9} & {8} \\{-6}&{-4}&{5}\ \\ {5} & {0} & {-4}\end{array}\right].$$
