Explanation:

- Option 1: A symmetric matrix

This is incorrect because the inverse of a skew-symmetric matrix isn't guaranteed to be symmetric.

- Option 2: A skew-symmetric matrix

The inverse of a skew-symmetric matrix isn't skew-symmetric, as skew-symmetric properties don't typically transfer to the inverse.

- Option 3: Diagonal matrix

This is false, since a diagonal form isn't a necessity for the inverse of skew-symmetric matrices.

- Option 4: Does not exist

A skew-symmetric matrix of odd order has a determinant of zero, meaning it is singular and not invertible.