Please help me with this problem, thank you so much!!!

Question 19. Here are a couple of new denitions: An n x 11 matrix A is symmetric provided AT = A and skew-symmetric provided AT = A. (1) Give examples of symmetric and skew-symmetric 2 x 2, 3 x 3, and 4 x 4 matrices. (2) What can you say about the main diagonal of a skew-Symmetric matrix? (3) Give an example of a matrix that is both symmetric and skew-symmetric. (4) Prove that for any n x n matrix A, the matrices A + AT, AAT, and ATA are symmetric and A AT is skew-symmetric. (5) Prove that any n x n can be written as the sum of a symmetric and skewsymmetric matrices. Hint: Did you do part (4) yet