Answer
$\left[\begin{array}{cccc}
{-22}&{29}&{8}&{-1}\\
{-10}&{17}&{6}&{-1}\end{array}\right]$
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 $2$ by $\fbox{$2$}$ matrix and B is a $\fbox{$2$}$ by $4$ matrix.
The product $AB$ is defined, and is a $2$ by $4$ matrix.
$AB=$
$\left[\begin{array}{llll}
(4)(-6)+(1)(2) & (4)(6)+(1)(5) & (4)(1)+(1)(4) & (4)(0)+(1)(-1)\\
(2)(-6)+(1)(2) & (2)(6)+(1)(5) & (2)(1)+(1)(4) & (2)(0)+(1)(-1)
\end{array}\right]$
$=\left[\begin{array}{cccc}
{-22}&{29}&{8}&{-1}\\
{-10}&{17}&{6}&{-1}\end{array}\right]$
