# Math Help - prove

1. ## prove

Assume that alpha:S-T, and beta: T-U, gamma: T-U. prove each of the following statements

A) If alpha and beta are invertible, then beta of alpha is invertible.

2. Originally Posted by mandy123
Assume that alpha:S-T, and beta: T-U, gamma: T-U. prove each of the following statements

A) If alpha and beta are invertible, then beta of alpha is invertible.
I do the first one.
A function is invertible if and only if it is one-to-one.
Say $\beta (\alpha (x) ) = \beta(\alpha(y)) \implies \alpha(x) = \alpha(y) \implies x=y$.
Thus, $\beta \circ \alpha$ is invertible.