A Matrix Problem

Algebra Level 3

Read the following statements carefully.

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

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

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

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

Which of the following statements are correct?

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