Answer
To multiply two matrices,
the first must have as many columns as the other has rows.
The product of an $m\times n$ matrix $A$ and an $n\times p$ matrix $B$
is an $m\times p$ matrix $AB$.
The element in the ith row and $j\mathrm{t}\mathrm{h}$ column of $AB$ is found by
multiplying each element in the ith row of $A$
by the corresponding element in the $j\mathrm{t}\mathrm{h}$ column of $B$
and adding the products.
(example provided in the step-by-step section)
Work Step by Step
To multip;y two matrices,
the first must have as many columns as the other has rows.
The product of an $m\times n$ matrix $A$ and an $n\times p$ matrix $B$ is an $m\times p$ matrix $AB$.
The element in the ith row and $j\mathrm{t}\mathrm{h}$ column of $AB$ is found by
multiplying each element in the ith row of $A$
by the corresponding element in the $j\mathrm{t}\mathrm{h}$ column of $B$
and adding the products.
Example
A$=\left[\begin{array}{lll}
1 & 2 & 3\\
4 & 5 & 6
\end{array}\right]$ is a 2$\times$3 matrix
B$= \left[\begin{array}{ll}
1 & 2\\
3 & 4\\
5 & 6
\end{array}\right]$ is a 3$\times$2 matrix, so
$AB$ is defined, and is a 2$\times$2 matrix.
Let $AB=C=[c_{ij}]$
$c_{21}$= (2nd row of A) times (first column of B)
=$ 4(1)+5(3)+6(5)=4+15+30=49$
