True or False. Please provide brief reasons.

a)Only square matrices are invertible.

b)Only square matrices have transposes.

c)If A is a 2 x 3 matrix (i.e., with 2 rows and 3 columns) and B is 3 x 5, then (AB)^T is 5 x 2.

d)If a matrix A has column 1 + column 2 = column 3, then A is invertible.