Every matrix can be represented as a sum of symmetric and skew symmetric matrices

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.

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

If a symmetric /skew symmetric matrix is expressed as a sum of a symmetric and a skew symmetric matrix then prove that one of the matrices in the sum must be zero matrix .

Prove that the square matrix [{:(5,2),(3,-6):}] can be expressed as a sum of symmetric and skew- symmetric matrices.

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

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

Express as a sum of a symmetric and a skew symmetric matrix: [[0,1],[1,0]]

Express as a sum of a symmetric and a skew symmetric matrix: [[1,5],[7,-3]]