# Given A=((-1, 2), (3, 4)) and B=((-4, 3), (5, -2)), how do you find AB?

Sep 26, 2016

$\text{AXB} = \left(\begin{matrix}14 & - 7 \\ 8 & 1\end{matrix}\right)$

#### Explanation:

Check first whether the matrices are compatible?

$\textcolor{b l u e}{2} \text{X"color(red)(2) and color(red)(2)"X} \textcolor{b l u e}{2}$

are compatible (the middle numbers in red are the same)
and will give a $\textcolor{b l u e}{2 X 2}$ matrix

The elements in each ROW in A must be multiplied by the elements of the COLUMNS of B, then find the sum each time.

$A = \left(\begin{matrix}- 1 & 2 \\ 3 & 4\end{matrix}\right)$ and $B = \left(\begin{matrix}- 4 & 3 \\ 5 & - 2\end{matrix}\right)$

The separate calculations give:

$\textcolor{w h i t e}{\times} 4 \textcolor{w h i t e}{\times x} - 3 \textcolor{w h i t e}{\times x} - 12 \textcolor{w h i t e}{\times x . x} 9$
$\textcolor{w h i t e}{x} \underline{10} \textcolor{w h i t e}{\times \times} \underline{- 4} \textcolor{w h i t e}{\times \times x} \underline{20} \textcolor{w h i t e}{\times x} \underline{- 8}$
$\textcolor{w h i t e}{x} 14 \textcolor{w h i t e}{x . \times} - 7 \textcolor{w h i t e}{\times x . \times} 8 \textcolor{w h i t e}{\times x . x} 1$

$\text{AXB} = \left(\begin{matrix}14 & - 7 \\ 8 & 1\end{matrix}\right)$