Are matrices A and B inverses

Question

A=[[-5,-18],[2,7]] and B=[[7,18],[-2,-5]]

Answer 1

To determine if two matrices are inverses, we can multiply them together and see if the result is the identity matrix.

Using matrix multiplication, we find that:

AB = [[-5*-2 + -18*-5, -5*7 + -18*-2], [2*-2 + 7*-5, 2*7 + 7*-2]]
= [[10 + 90, -35 + 36], [-4 - 35, 14 - 14]]
= [[100, 1], [-39, 0]]

The resulting matrix is not the identity matrix, so matrices A and B are not inverses of each other.