UPSC NDA Math Model Paper 2

Since A is an skew-symmetric matrix, we must have:
AT=−A
Because A is given to be invertible, on taking the inverse of both sides, we get:
(AT)−1=(−A)−1
We also know that
(AT)−1=(A−1)T.
∴(A−1)T=−(A−1)
Since the transpose of A−1 is equal to its negative, A−1 is a skew-symmetric matrix.