If , and show that is skew-symmetric

Solution:

We have .
The transpose of the matrix is an operation of making interchange of elements by the rule on positioned element shifted to new position .
The symmetric matrix is defined as similarity of transpose of matrix with it self. i.e, .

The skew-symmetric matrix is defined as similarity of transpose of matrix with it self. i.e, .

Therefore finally we have

Here
Therefore is skew symmetric.