8. The number of A in T, such that ...
Question

# 8. The number of A in T, such that the trace of A is not divisible by p but det (A) is divisible by pis (a) (p-1)(p2-p+1) (b) p8 - (p-1)2 (c) (p-1)2 (d) (p-1) (p2-2)

JEE/Engineering Exams
Maths
Solution
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( rightarrow ) Frace of ( A=2 a ). will te divinite of ( p ) [ begin{array}{l} y quad y=20 1 A 1=a^{2}-6 c end{array} ] for ( left(a^{2}-b cright) ) to be divinite of ( p ) ordured pabrs ". there are exactly ( (p-1) ) a ( (8, c) ) for any [ therefore operatorname{Req} cdot n 0 cdot ln (p-1)^{2} ]