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Let $p$ be an odd prime number and $T_p$ is the following set of $2 \times 2$ matrices: $$ T_p = \left\{ A = \begin{bmatrix} a & b \\ c & a \end{bmatrix}\ \Biggm|a,b,c \in \{0,1,2,...(p-1)\} \right\}$$

then how to prove that the number $k$ of $A$ in $T_p$ such that the trace of A is not divisible by $p$ but the $det(A)$ is divisible by $p$, is $k=(p-1)^2$ ?

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    @Debanjan: Four months in, must you post in the imperative mode?2011-01-31
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    @Arturo: I think $(p-1)^2$ is the number of matrices in $T_p$.2011-01-31
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    @PEV: Yeah, I got it finally; $(p-1)^2$ is meant to be the number of elements in $T_p$ that satisfy the given condition; I've rephrased to clarify that.2011-01-31
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    @Arturo Magidin:I don't get your first comment :)2011-01-31
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    @Debanjan: Your original post was written as if it were an assignment/order, written in the imperative mode ("Show...", "Prove..."). You have been here for four months, by now you should know not to do that, even fleetingly.2011-01-31
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    @ Arturo Magidin: Oopps,I was just typing from my question paper so .. eventually it is going to be fixed :)2011-01-31

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