1. A matrix \( \mathbf{M} \) is called a skew symmetric if \( \mathbf{M}^{\mathrm{T}} = -\mathbf{M} \). Prove that if \( \mathbf{A} \) is an \( n \times n \) skew symmetric matrix and \( n \) is odd, then \( \mathbf{A} \) is singular. (12%)