Mark each of the following statements true or false:
(a) For any matrix A, both AA^T and A^TA are defined.
(b) If A and B are matrices such that AB = O and A ≠ O, then B = O.
(c) If A, B, and X are invertible matrices such that XA = B, then X = A^-1 B.
(d) The inverse of an elementary matrix is an elementary matrix.
(e) The transpose of an elementary matrix is an elementary matrix.
(f) The product of two elementary matrices is an elementary matrix.
(g) If A is an m  n matrix, then the null space of A is a subspace of Rⁿ.
(h) Every plane in R³ is a two-dimensional subspace of R³.
(i) The transformation T: R² → R² defined by T(x) = -x is a linear transformation.
(j) If T : R⁴ → R⁵ is a linear transformation, then there is a 4 × 5 matrix A such that T(x) = Ax for all x in the domain of T.