Question

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

Answer 1

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

`(-4*-6)+(5*1/2)` will be the upper left element
`(-4*2)+(5*3/4)` will be the upper right element
`(3*-6)+(2*1/2)` will be the lower left element
and
`(3*2)+(2*3/4)` will be the lower right element.

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

`(53/2, -17/4)`
`(-17, 15/2)`