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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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field, fields, invertible, martices 
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