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

Question

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 (A) 4 (B) 5 (C) 6 (D) 12

Tardigrade Admin · Accepted Answer

∵ A is skew symmetric ⇒ a=c=0 |A|=b2 ∵ |A| is divisible by 3 ⇒ b can be 0,3,6,9,12 (five possibilities)

Q. 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

$4$

$5$

$6$

$12$

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

Q. Consider a skew-symmetric matrix A=[a−b​bc​] 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

4

5

6

12

∵ A is skew symmetric ⇒a=c=0 ∣A∣=b2 ∵∣A∣ is divisible by 3 ⇒b can be 0,3,6,9,12 (five possibilities)

Q. 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

$4$

$5$

$6$

$12$

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