Which of the following statements is/are correct?
I. Adjoint of a unit matrix is a unit matrix.
II. \( A (\text{adj } A) = (\text{adj } A) A = |A|I \)
III. Adjoint of a symmetric matrix is symmetric.
IV. Adjoint of a diagonal matrix is a diagonal matrix.
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The adjoint of a unit matrix is a unit matrix, and the adjoint of a symmetric or diagonal matrix retains the symmetry or diagonal structure.