# If A=((-4, 5),(3, 2)) and B=((-6, 2), (1/2, 3/4)), what is AB?

Oct 18, 2014

Multiply each row of the first matrix by each column of the second matrix.

$\left(- 4 \cdot - 6\right) + \left(5 \cdot \frac{1}{2}\right)$ will be the upper left element
$\left(- 4 \cdot 2\right) + \left(5 \cdot \frac{3}{4}\right)$ will be the upper right element
$\left(3 \cdot - 6\right) + \left(2 \cdot \frac{1}{2}\right)$ will be the lower left element
and
$\left(3 \cdot 2\right) + \left(2 \cdot \frac{3}{4}\right)$ will be the lower right element.

Cleaning up we get $\left(24 + \frac{5}{2} = \frac{52}{2}\right)$ upper left
$\left(- 8 + \frac{15}{4} = - \frac{17}{4}\right)$ upper right,
$\left(- 18 + 1 = - 17\right)$ lower left and,
$\left(6 + \frac{1}{2} = \frac{15}{2}\right)$ for lower right.

$\left(\frac{53}{2} , - \frac{17}{4}\right)$
$\left(- 17 , \frac{15}{2}\right)$