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IIT JEE Advanced 2010 Paper 1

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Paragraph for Questions 72–74:
Let p be an odd prime number and Tp be the following set of 2 × 2 matrices:

Tp = {A=[

a	b
c	d

]:a,b,c∊{0,1,...,p−1}}

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Question : 73

Total: 84

The number of A in Tp such that the trace of A is not divisible by p bu t det (A) is divisible by p is
(Note: The trace of a matrix is the sum of its diagonal entries.)

(p − 1) (p2 − p + 1)
p3−(p−1)2
(p−1)2
(p−1)(p2−2)

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