Matrices and Determinants 1 Question 18

18. The number of A in Tp such that the trace of A is not divisible by p but det(A) is divisible by p is

(a) (p1)(p2p+1)

(b) p3(p1)2

(c) (p1)2

(d) (p1)(p22)

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Answer:

Correct Answer: 18. (c)

Solution:

  1. Trace of A=2a, will be divisible by p, iff a=0.

|A|=a2bc, for (a2bc) to be divisible by p.

There are exactly (p1) ordered pairs (b,c) for any value of a.

Required number is (p1)2.



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