Prove that any square matrix can be expressed as sum of symmetric and skew symmetric matrix uniquely

State True/False: Every rectangular matrix can be expressed as sum of symmetric and skew symmetric matrices.

State whether it is true or false: every square Matrix can be represented as sum of symmetry and skew symmetric matrix.

…….. Matrix is both symmetric and skew symmetric matrix .

Express [[5,1],[7,0]] as sum of symmetric and skew-symmetric matrices.

Express [[2,1],[3,0]] as sum of symmetric and skew-symmetric matrices.

Express [[2,1],[-1,8]] as sum of symmetric and skew-symmetric matrices.

If a matrix is both symmetric and skew-symmetric matrix, then

Express the following matrices as the sum of a symmetric and a skew symmetric matrix :