Indicate whether the statement is always true or sometimes false. Justify your answer with a logical argument or a counterexample.
(a) If A is a singular n × n matrix, then Ax = 0 has infinitely many solutions.
(b) If A is a singular n × n matrix, then the reduced row-echelon form of A has at least one row of zeros.
(c) If A is a singular n × n matrix, and B results by interchanging two rows of A, then B may or may not be singular.