How can I show that the number of $2 \times 2$ matrices over the field of three elements with determinant $1$ is $24$?
Number of $2 \times 2$ matrices over the field with $3$ elements, with determinant $1$
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linear-algebra
matrices
finite-fields
linear-groups
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0The question is taken from IIT-JAM 2010 question paper – 2017-01-07
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1Isn't it $\Bbb{Z}_3$? – 2017-01-07
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0This question also has an answer here : http://math.stackexchange.com/questions/1353991/determining-the-cardinality-of-sl-2-f-3?noredirect=1&lq=1 – 2017-01-07