Answer the following statements by True or False.

Give proper explanation to support your answers.

(a) For every matrix A, A^TA = AA^T .

(b) All of the singular values of a matrix are non-negative.

(c) Every m n matrix has a unique Singular Value Decomposition.

(d) Only nonsingular square matrices have pseudoinverses.

(e) For a non singular matrix, its pseudoinverse must equal to its inverse.