Linear Algebra - Matrices

A is an $m \times m$ skew-symmetric matrix with real-valued entries, and $x$ is an $m$-dimensional column vector with real-valued entries such that $x^T x = 1$. The quantity $x^T A x$ evaluates to ________ (Answer in int...

Consider an $n \times n$ orthogonal matrix $A$ with real entries and each column having unit Euclidean norm. Which of the following statements is/are correct?

Which one of the following matrices has an inverse?