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.