Finite Math: Matrices

Question

Let F = [0, 1, 1, 2, 0, 1, 0, 2, 3], and G = [1, 1/2, -1/2, 3, 0, -1, -2, 0, 1]

Are F and G inverses of each other? Why?

Answer 1

The product of

0 1 1 1 1/2 -1/2

2 0 1 and 3 0 -1

0 2 3 -2 0 1

is

1 0 0

0 1 0

0 0 1

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The product of

1 1/2 -1/2 0 1 1

3 0 -1 and 2 0 1

-2 0 1 0 2 3

1 0 0

0 1 0

0 0 1

so yes they are inverses because BOTH of their products are the identity matrix