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Matrices and Determinants question

2010 · Shift 1 · Q56

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JEE Advanced
Mathematics
Matrices and Determinants
2010 · Shift 1 · Q56

Matrices and Determinants question

2010 · Shift 1 · Q56

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

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

is not divisible by

p

is :

A
$2 p^2$
B
$p^3-5 p$
C
$p^3-3 p$
D
$p^3-p^2$

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