Answer
$\begin{bmatrix}
14&7&-2\\
20&12&-4\\
-14&7&-6
\end{bmatrix}$
Work Step by Step
$\begin{bmatrix}
4&1\\
6&2\\
-2&3
\end{bmatrix}\times\begin{bmatrix}
4&1&0\\
-2&3&-2
\end{bmatrix}:$
Let the resultant be matrix M.
$\implies M_{1,1} = (4)(4)+(1)(-2) = 14$
$\implies M_{1,2} = (4)(1)+(1)(3) = 7$
$\implies M_{1,3} = (4)(0)+(1)(-2) = -2$
$\implies M_{2,1} = (6)(4)+(2)(-2) = 20$
$\implies M_{2,2} = (6)(1)+(2)(3) = 12$
$\implies M_{2,3} = (6)(0)+(2)(-2) = -4$
$\implies M_{3,1} = (-2)(4)+(3)(-2) = -14$
$\implies M_{3,2} = (-2)(1)+(3)(3) = 7$
$\implies M_{3,3} = (-2)(0)+(3)(-2) = -6$
$\therefore M = \begin{bmatrix}
14&7&-2\\
20&12&-4\\
-14&7&-6
\end{bmatrix}$
