Invertible Integers under Multiplication/Corollary 1
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Corollary to Invertible Integers under Multiplication
Let $a, b \in \Z$ such that $a b = 1$.
Then $a = b = \pm 1$.
Let $a b = 1$.
So by Invertible Integers under Multiplication, $a = \pm 1$ and $b = \pm 1$.
As $-1 \times 1 = -1$, it follows that either:
- $a = b = 1$
- $a = b = -1$.