Question

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

Answer 1

`"AXB" = ((14, -7), (8, 1))`

Explanation:

Check first whether the matrices are compatible?

`color(blue)(2)"X"color(red)(2) and color(red)(2)"X"color(blue)(2)`

are compatible (the middle numbers in red are the same)
and will give a `color(blue)(2X2)` 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=((-1, 2), (3, 4))` and `B=((-4, 3), ( 5, -2))`

The separate calculations give:

`color(white)(xx)4color(white)(xxx)-3color(white)(xxx)-12color(white)(xxx.x)9`
`color(white)(x)ul10color(white)(xxxx)ul(-4)color(white)(xxxxx)ul20color(white)(xxx)ul(-8)`
`color(white)(x)14color(white)(x.xx)-7color(white)(xxx.xx)8color(white)(xxx.x)1`

`"AXB" = ((14, -7), (8, 1))`