JEE (Advanced) 2010 Paper-1

Instructions

Let p be an odd prime number and $$T_p$$ be the following set of $$2 \times 2$$ matrices:

$$T_p = \left\{A = \begin{bmatrix}a & b \\c & a \end{bmatrix}:a, b, c \in \left\{0, 1, 2, ...., p-1\right\}\right\}$$

Question 44

The number of A in $$T_p$$, such that det (A) is not divisible byp is


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