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 September 16th, 2014, 08:58 PM #1 Newbie   Joined: Sep 2014 From: Canada Posts: 2 Thanks: 0 Invertible Martices Let $\displaystyle S$ be a set of $\displaystyle d \times d$ matrices of a field of order $\displaystyle q$, such that the difference of any two distinct matrices in $\displaystyle S$ is invertible. Prove that $\displaystyle |S| \leq q^d.$ I know that the set of $\displaystyle d \times d$ matrices is equal to $\displaystyle q^d$ so this question seems trivial and I don't know where to start.
 September 16th, 2014, 11:12 PM #2 Newbie   Joined: Sep 2014 From: Canada Posts: 2 Thanks: 0 The set of dxd matrices would have cardinality $\displaystyle q^{d^2}$ but I don't know where to go from there.

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