Question

What must be true of every diagonal element of a skew-symmetric matrix?

Options

• All diagonal elements are positive.

• All diagonal elements are one.

• All diagonal elements are zero.

• All diagonal elements are equal to the corresponding off-diagonal elements.

Answer 1

For a diagonal entry, \[a_{ii}=-a_{ii}\] in a skew-symmetric matrix. This gives \[2a_{ii}=0\], so every diagonal element is zero.