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

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

The inverse of an invertible symmetric matrix is a symmetric matrix.

A is symmetric matrix if A^T =

Which of the following is/are incorrect? (i) adjoint of a symmetric matrix is symmetric (ii) adjoint of a unit matrix is a unit matrix (iii) A (adj A)=(adj A)A=absAI (iv) adjoint of a diagonal matrix is a diagonal matrix

Express the matrix A=[{:(3,-4),(1,-1):}] as the sum of a symmetric matrix and a skew-symmetric matrix.

Express the matrix A=[{:(2,3),(-1,4):}] as the sum of a symmetric matrix and a skew-symmetric matrix.

The inverse of a skew symmetric matrix is

If A is skew-symmetric matrix then A^(2) is a symmetric matrix.

Let A and B be symmetric matrices of same order. Then A+B is a symmetric matrix, AB-BA is a skew symmetric matrix and AB+BA is a symmetric matrix