Answer
$\left[\begin{array}{rr}
28 & -9\\
4 & 23
\end{array}\right]$
Work Step by Step
A is a 2 by 3 matrix. C is a 3 by 2 matrix.
AC is defined and is a 2 by 2 matrix,
the entry $[AC]_{ij}$ = (row i of A)$\times$(column j of B)
$AC=\left[\begin{array}{lll}
0 & 3 & -5\\
1 & 2 & 6
\end{array}\right]\left[\begin{array}{ll}
4 & 1\\
6 & 2\\
-2 & 3
\end{array}\right]$
$=\left[\begin{array}{cc}
{0(4)+3(6)+(-5)(-2)}&{0(1)+3(2)+(-5)(3)}\\
{1(4)+2(6)+6(-2)}&{1(1)+2(2)+6(3)}\end{array}\right]$
$=\left[\begin{array}{ll}
0+18+10 & 0+6-15\\
4+12-12 & 1+4+18
\end{array}\right]$
$=\left[\begin{array}{rr}
28 & -9\\
4 & 23
\end{array}\right]$
