Q16 / 124 · NTA Abhyas (JEE Main) 2020 · Mathematics · Determinants

Let $A = [\begin{matrix} a & b \\ c & a \end{matrix}] \forall a, b, c, \in \{0, 1, 2\}$ . If $A$ is a singular matrix, then the number of possible matrices $A$ are

A
$18$
B
$27$
Correct answer
C
$7$
D
$3$

Solution

|A| = a^{2} - b c = 0

(for a singular matrix)

\Rightarrow a^{2} = b c

7

cases

\{\begin{matrix} a = 0, b = 0, c = 0, 1, 2 \\ a = 0, b = 1, 2, c = 0 \\ a = 1, b = 1, c = 1 \\ a = 2 b = 2 c = 2 \end{matrix}

Hence, total number of possible matrices

= 7

Hence, the correct answer is option: 'C'.

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