Prove that adjoint of a symmetric matrix is also a symmetric matrix.

Which of the following is/are correct ? (i) Adjoint of a symmetric matrix is also a symmetric matrix. (ii) Adjoint of a diagonal matrix is also a diagonal matrix. (iii) If A is a square matrix of order n and lambda is a scalar, then adj ( lambda A)= lambda^(n) adj(A) (iv) A (adj A) = (adj A) A = |A| I

Which of the following is/are correct? (i) Adjoint of a symmetric matrix is is also a symmetric matrix (ii) Adjoint of a diagonal matrix is also a diagonal matrix. (iii) If A is a square matrix of order n and lamda is a scalar, then adj(lamdaA)=lamda^(n)adj(A) . (iv) A(adjA)=(adjA)A=|A|I

Prove that square matrix can be expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

Prove that every square matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

Prove that every square matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

Prove that every square matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix.