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

Jul 20, 2016

$B A = \left(\begin{matrix}13 & 4 \\ - 11 & 2\end{matrix}\right)$

#### Explanation:

To multiply matrices:

1. . Are they compatible?
These are both 2 X 2, Yes, The answer will also be 2 X 2.

2. Correct order. AB is not the same as BA

3. Multiply each value in a row in turn BY the values in a column and add the answers.

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

The calculations are :

top row x first column: $- 4 \cdot - 1 + 3 \cdot 3 = 4 + 9 = 13$
top row x second column:$- 4 \cdot 2 + 3 \cdot 4 = - 8 + 12 = 4$
bottom row x first column:$5 \cdot - 1 \cdot + - 2 \cdot 3 = - 5 - 6 = - 11$
bottom row x second column:$5 \cdot 2 + 2 \cdot 4 = 10 - 8 = 2$

$B A = \left(\begin{matrix}13 & 4 \\ - 11 & 2\end{matrix}\right)$