數學(A)

(5%) How many of the following statements are true?

• The inverse of an orthogonal matrix is orthogonal.
• The product of two orthogonal matrices is an orthogonal matrix.
• Every matrix with orthonormal columns is invertible.
• If $A, B \in \mathbf{R}^{n\times n}$, and $A + iB$ is a unitary matrix, then $A^TB$ is symmetric.