For this exercise assume that the matrices are all n xn. The statement in this exercise is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer. If the equation Ax = 0 has a nontrivial solution, then A has fewer than n pivot positions. Choose the correct answer below. O A. The statement is false. By the Invertible Matrix Theorem, if the equation Ax = 0 has a nontrivial solution, then matrix A is invertible. Therefore, A has n pivot positions. O B. The statement is true. By the Invertible Matrix Theorem, if the equation Ax = 0 has a nontrivial solution, then matrix A is not invertible. Therefore, A has fewer than n pivot positions. O C. The statement is false. By the Invertible Matrix Theorem, if the equation Ax = 0 has a nontrivial solution, then the columns of A do not form a linearly independent set. Therefore, A has n pivot positions. O D. The statement is true. By the Invertible Matrix Theorem, if the equation Ax = 0 has a nontrivial solution, then the columns of A form a linearly independent set. Therefore, A has fewer than n pivot positions