Mark each statement True or False. Justify each answer.
a. Every symmetric matrix is orthogonally diagonalizable.
b. If B = PDPT, where P T = P-1 and D is a diagonal matrix, then B is a symmetric matrix.
c. An orthogonal matrix is orthogonally diagonalizable.
d. The dimension of an eigenspace of a symmetric matrix equals the multiplicity of the corresponding eigenvalue.