Which of the following is true?

(A) A linear transformation with codomain

is onto if and only if the rank of its standard
matrix is m.

(B) A linear transformation is one-to-one if and only if its null space consists only of the zero
vector.

(C) A linear transformation is onto if and only if the columns of its standard matrix form a
generating set for its range.

(D) If the composition UT of two linear transformations T :

and U :

is
defined, then m = p must be true and the composition UT is also a linear transformation.

(E) For every invertible linear transformation T, the function

is also a linear transfor-
mation.