Given the following matrices with specified sizes.

A B C D E
(4 x 5) (4 x 5) (5 x 2) (4x2) (5 x 4)

In each part, determine whether the given matrix expression is defined. For those that are defined, give the size of the resulting matrix.

(a) BA
(b) ABᵀ
(c) AC + D
(d) E(AC)
(e) A-3Eᵀ
(f) E(5B+A)