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- Jan 26, 2012

- 995

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**Problem**: Let $V$ be a finite-dimensional vector space over a finite field $\mathbb{F}_q$ of cardinality $q$. Let $\mathscr{B}$ be the set of ordered bases of $V$. Compute the cardinality of $\mathscr{B}$, as a formula involving $q$ and $\mathrm{dim}(V)$.

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