Group of Unitary Matrices under Multiplication is not Abelian

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Theorem

Let $n > 1$ be a natural number.

Then the group of unitary matrices $\map U n$ is not abelian.

Proof

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Sources

• 1974: Robert Gilmore: Lie Groups, Lie Algebras and Some of their Applications ... (previous) ... (next): Chapter $1$: Introductory Concepts: $1$. Basic Building Blocks: $2$. GROUP