Question

How do you multiply the matrices `((2, 3), (1, -3))` with `((-1, 0, 2), (0, 2, 3))`?

Answer 1

`((-2,6,13),(-1,-6,-7))`

Explanation:

Remember when multiplying matrices each entry in the product matrix are form by the corresponding
`color(white)("XXX")`row from the first matrix, and
`color(white)("XXX")`column from the second matrix

`((color(red)(2),color(red)(3)),(color(blue)(1),color(blue)(-3)))xx((color(brown)(-1),color(cyan)(0),color(orange)(2)),(color(brown)(0),color(cyan)(2),color(orange)(3)))`

#=( (color(red)(2)(color(brown)(-1))+color(red)(3)(color(brown)(0)), color(red)(2)(color(cyan)(0))+color(red)(3)(color(cyan)(2)), color(red)(2)(color(orange)(2))+color(red)(3)(color(orange)(3))), (color(blue)(1)(color(brown)(-1))+(color(blue)(-3))(color(brown)(0)),color(blue)(1)(color(cyan)(0))+(color(blue)(-3))(color(cyan)(2)),color(blue)(1)(color(orange)(2))+(color(blue)(-3))(color(orange)(3))) )#

`=((-2,6,13),(-1,-6,-7))`