NIMCET 2018 — Mathematics PYQ

Calculation:

Since A is a skew-symmetric matrix, we must have
$$A^T=-A$$  

Because A is given to be invertible, on taking the inverse of both sides, we get:
$$(A^T{)}^{-1}=(-A{)}^{-1}$$  

We also know that   
$$(A^T{)}^{-1}=(A^{-1}{)}^T$$  

Therefore, 
$$(A^{-1}{)}^T=-(A^{-1})$$  

Since the transpose of $A^{-1}$ \text{ is equal to its negative, } $A^{-1}$ is a skew-symmetric matrix.