1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider a skew-symmetric matrix A=[ a b -b c ] such that a, b and c are selected from the set S= 0, 1 , 2, 3 , . . . . . . . . 12 . If |A| is divisible by 3 , then the number of such possible matrices is

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Q. Consider a skew-symmetric matrix $A=\begin{bmatrix} \, \, a & \, b \\ -b & \, c \end{bmatrix}$ such that $a, \, b$ and $c$ are selected from the set $S=\left\{0, \, 1 , \, 2, \, 3 , . . . . . . . . 12\right\}.$ If $\left|A\right|$ is divisible by $3$ , then the number of such possible matrices is

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Solution:

$\because $ $A$ is skew symmetric $\Rightarrow a=c=0$
$\left|A\right|=b^{2}$
$\because \left|A\right|$ is divisible by $3$
$\Rightarrow b$ can be $0,3,6,9,12$ (five possibilities)