Is the Iverse of Skewed-Symmetric, Invertible Matrix A also Skewed-Symmetric

A is invertible, skewed symmetric

Transpose(A) = -(A)

Is Inverse(A) skewed symmetric?

Does Transpose(Inverse(A)) = -Inverse(A)?

Re: Is the Iverse of Skewed-Symmetric, Invertible Matrix A also Skewed-Symmetric

Let A be an nxn matrix. Assume that A is skew-symmetric. Then A^T = -A. The question is whether A^-1 is skew-symmetic. The answer is yes simply because of the fact that (A^-1)^T = (A^T)^-1. Note that

(A^-1)^T = (A^T)^-1 = (-A)^-1 = -A^-1