# For what value of x, is the matrix A=$\begin{bmatrix}0 & 1 & -2\\-1 & 0 & 3\\x & -3 & 0\end{bmatrix}$ a skew-symmetric matrix?

This question appeared in 65-1,65-2 and 65-3 versions of the paper in 2013.

Toolbox:
• A square matrix $A=$[a$_{ij}$] is said to be skew symmetric if $A'=-A$, that is $[a_{ij}]= -[a_{ji}]$ for all possible value of $i$ and $j$.
Given a matrix $A = \begin{bmatrix}0 & 1 & -2\\-1 & 0 & 3\\x & -3 & 0\end{bmatrix}$.
A square matrix $A=$[a$_{ij}$] is said to be skew symmetric if $A'=-A$, that is $[a_{ij}]= -[a_{ji}]$ for all possible value of $i$ and $j$.
Therefore, if $A$ were skew symmetric, then $x$ which is element $[a_{13}]$ must be equal to elment $-[a_{31}]$
Given $[a_{31}] = -2 \rightarrow x =-[a_{31}] = 2$