Please can you help me out with this question. Could you tell me the answers? It would be greatly appreciated.

Please can you help me out with this question. Could you tell me the answers? It would be greatly appreciated.

A is an n xn matrix. Determine whether the statement below is true or false. Justify the answer. A matrix A is not invertible if and only if 0 is an eigenvalue of A. Choose the correct answer below. O A. The statement is true. If 0 is an eigenvalue of A, then there are nontrivial solutions to the equation Ax = 0x. The equation Ax = Ox is equivalent to the equation Ax = 0, and Ax = 0 has nontrivial solutions if and only if A is not invertible. O B. The statement is false. If 0 is an eigenvalue of A, then the equation Ax = Ox has only the trivial solution. The equation Ax = Ox is equivalent to the equation Ax = 0, and Ax = 0 has only the trivial solution if and only if A is invertible. O C. The statement is true. If 0 is an eigenvalue of A, then the equation Ax = Ox has only the trivial solution. The equation Ax = 0x is equivalent to the equation Ax = 0, and Ax = 0 has only the trivial solution if and only if A is not invertible. O D. The statement is false. If 0 is an eigenvalue of A, then there are nontrivial solutions to the equation Ax = 0x. The equation Ax = 0x is equivalent to the equation Ax = 0, and Ax = 0 has nontrivial solutions if and only if A is invertible