How can I show that the number of $2 \times 2$ matrices over the field of three elements with determinant $1$ is $24$?
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The question is taken from IIT-JAM 2010 question paper – Austin20 Jan 07 '17 at 07:03
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1Isn't it $\Bbb{Z}_3$? – Red Banana Jan 07 '17 at 07:05
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This question also has an answer here : http://math.stackexchange.com/questions/1353991/determining-the-cardinality-of-sl-2-f-3?noredirect=1&lq=1 – Arnaud D. Jan 07 '17 at 14:49