True/false and explain your answers. a) rank (a + b) greaterthanorequalto rank a + rank b b) (ab)^2 = a^2 b^2 c) if a is not the zero matrix then a^2 cannot be the zero matrix. d) every elementary matrix is symmetric. e) every real diagonal matrix is hermitian. f) (ca)^t = ca^t g) (ab)^t = a^t b^t h) rank ab = min(rank a, rank b) i) every tridiagonal matrix is symmetric.