If $A=\begin{bmatrix}0&x^2-6&-3\\-x&0&-8\\x^2-2x&8&0\end{bmatrix}$ is a skew symmetric matrix, then the value(s) of $x$ is/are-
(A) 3
(B) -3
(C) -2
(D) -1
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) only **
Matrix
$A=\begin{bmatrix}0 & x^{2}-6 & -3\\ -x & 0 & -8\\ x^{2}-2x & 8 & 0\end{bmatrix}$
Skew–symmetry requires $a_{ij}=-a_{ji}$ for all $i\ne j$.
From $(1,2)$ and $(2,1)$: $x^{2}-6 = -(-x)\Rightarrow x^{2}-x-6=0$
So $x=3$ or $x=-2$.
From $(1,3)$ and $(3,1)$: $x^{2}-2x = -(-3)\Rightarrow x^{2}-2x-3=0$
So $x=3$ or $x=-1$.
Common solution: $x=3$.
Answer: $x=3$