Question

Which of the following statement is always true?

(A) Adjoint of a symmetric matrix is a symmetric matrix

(B) Adjoint of a unit matrix is unit matrix

(C) A (adj A) = (adj A)A

(D) Adjoint of a diagonal matrix is diagonal matrix 

Answer 1

Answer is (A), (B), (C), (D)

By the properties of adjoint of a matrix, adjoint of a symmetric matrix is again a symmetric matrix.

Similarly,

A (adj A) = (adj A) A = |A|I

Also adjoints of unit and diagonal matrices are also unit and diagonal matrices.