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Question:

For what value of x is the matrix A a skew symmetric matrix?

Solution:

Given: A = 

0 1 x
1 0 3
x 3 0

is a skew matrix.
We know that any square matrix A = [aij] is said to be skew symmetric if AT = -A, that is [aij] = -[aji] for all possible values of i and j.
AT = 

0 1 x
1 0 3
x 3 0

= -A = 

0 -1 -x
-1 0 -3
-x -3 0

On comparing, we get x = -1
Therefore, the value of x will be -1.