8. Please answer TRUE or FALSE for the following statements (NO need to justify your answer). No credit for unanswered questions; incorrect answers will deduct the credit until zero point is earned in this section.

(a) (correct: 1; incorrect: -1; unanswered: 0) For any square real matrix $A$, $A^T + A$ is always symmetric.

(b) (correct: 1; incorrect: -1; unanswered: 0) For a square real matrix $A$, if $Ax = 0$ has a non-zero solution, then $A$ is invertible.

(d) (correct: 1; incorrect: -1; unanswered: 0) Let $A$ be a $m \times n$ real matrix, where $m < n$, with full row rank. $Ax = b$ has either 0 or 1 solution.

(j) (correct: 1; incorrect: -1; unanswered: 0) Let $A$ and $B$ be $n \times n$ real matrices. Then, $\text{rank}(AB) \le \min(\text{rank}(A), \text{rank}(B))$.