The number of A in Tp such that det (A) is not divisible by p is
A
p3−5p
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B
p3−p2
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C
2p2
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D
p3−3p
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Solution
The correct option is Bp3−p2 The number of matrices for which p does not divide Tr(A) is (p–1)p2 of these (p–1)2are such that p||A|. The number of matrices for which p divides Tr(A) and p does not divide |A| are (p–1)2. ∴ Required number is (p–1)p2–(p–1)2+(p–1)2=p3–p2