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Matrices and Determinants question

2010 · Shift 1 · Q55

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JEE Advanced
Mathematics
Matrices and Determinants
2010 · Shift 1 · Q55

Matrices and Determinants question

2010 · Shift 1 · Q55

JEE AdvancedMathematicsMatrices and DeterminantsMCQ+3 / −1

Let

p

be an odd prime number and

T_p

be the following set of

2 \times 2

matrices :

\mathrm{T}_{\mathrm{p}}=\left\{\mathrm{A}=\left[\begin{array}{ll} a & b \\ c & a \end{array}\right]: a, b, c \in\{0,1,2, \ldots, p-1\}\right\}

The number of A in

\mathrm{T}_p

such that the trace of A is not divisible by

p

but

\operatorname{det}(\mathrm{A})

is divisible by

p

is [Note : The trace of a matrix is the sum of its diagonal entries.]

A
$(p-1)\left(p^2-p+1\right)$
B
$p^3-(p-1)^2$
C
$(p-1)^2$
D
$(p-1)\left(p^2-2\right)$

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