A Matrix Problem

Algebra Level 3

Read the following statements carefully.

(1(1) The elements on the main diagonal of a symmetric matrix are all zero.

(2(2) The elements on the main diagonal of a skew-symmetric matrix are all zero.

(3(3) For any square matrix A,12(A+A)A, \dfrac{1}{2}(A + A') is skew-symmetric.

(4(4) For any square matrix A,12(AA)A, \dfrac{1}{2}(A - A') is skew-symmetric.

Which of the following statements are correct?

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