Answer
$\left[\begin{array}{rrr}
{-1}&{2}&{-1}\\
{0}&{-12}&{3}\\
{15}&{30}&{0}\end{array}\right]$
Work Step by Step
Let $A$ denote an $m$ by $\fbox{$r$}$ matrix and let $B$ denote an $\fbox{$r$}$ by $n$ matrix.
The product $AB$ is defined as the $m$ by $n$ matrix whose entry in row $i,$ column $j$
is the product of the $i$ th row of $A$ and the $j$ th column of $B$ .
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$A$ is a $3$ by $\fbox{$2$}$ matrix and B is a $\fbox{$2$}$ by $3$ matrix.
The product $AB$ is defined, and is a $3$ by $3$ matrix.
$AB=\left[\begin{array}{ccc}
{1(2)+(-1)(3)}&{1(8)+(-1)(6)}&{1(-1)+(-1)(0)}\\
{(-3)(2)+2(3)}&{(-3)(8)+2(6)}&{(-3)(-1)+2(0)}
\\{0(2)+5(3)}&{0(8)+5(6)}&{0(-1)+5(0)}\end{array}\right]$
$=\left[\begin{array}{rrr}
{-1}&{2}&{-1}\\
{0}&{-12}&{3}\\
{15}&{30}&{0}\end{array}\right]$
