Matrices and Determinants

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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}}

Section: Mathematics

Question : 51 of 56

Marks: +1, -0

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.)

[JEE Adv 2010 P1]

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

Validate

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