Question

How do you multiply `((2, -1), (3, 4))^4`?

Answer 1

`((-107, -84),(252,61))`

Explanation:

Just like with ordinary numbers `A^4 = A times A times A times A`. This looks like it may take three matrix multiplications, but we can actually do this in 2.

`A = ((2, -1), (3, 4)) implies`
`A^2 = ((2, -1), (3, 4))((2, -1), (3, 4)) = ((1, -6),(18,13))`
and thus
`A^4 =A^2 times A^2 = ((1, -6),(18,13))((1, -6),(18,13)) =((-107, -84),(252,61))`