Symmetric and Skew-symmetric Matrices

If the matrix $A$ is both symmetric and skew symmetric, then

If $A=\left[\begin{array}{ccc}2& 1& 1\\ -1& 0& 2\\ 0& 1& 3\end{array}\right]$ then prove that $A+A^T$ is symmetric matrix.

Express the matrix $A$ as the sum of symmetric and skew-symmetric matrix where $A=\left[\begin{array}{cc}6& 2\\ 5& 4\end{array}\right]$

The symmetric part of the matrix $\left[\begin{array}{ccc}1& 2& 6\\ 4& 3& -4\\ 8& 6& 5\end{array}\right]$ is

If $A=\left[\begin{array}{cc}3& x-1\\ 2x+3& x+2\end{array}\right]$ is a symmetric matrix, then x =

If $A=\left[\begin{array}{cc}5& x\\ y& 0\end{array}\right]$ and $A=A^T,$ then

If $A=\left[\begin{array}{ccc}2& 0& -3\\ 4& 3& 1\\ -5& 7& 2\end{array}\right]$ is expressed as the sum of a symmetric and skew-symmetric matrix then the symmetric matrix is 

If $\mathrm{A}$ is a skew-symmetric matrix, then trace of $\mathrm{A}$ is

A skew symmetric matrix $S$ satisfies the relation $S^2+I=0$, where $I$ is a unit matrix, then $S{S}^{\text{'}}$ is (where $S^{\text{'}}$ is transpose of $S$)

If $A$ is a skew-symmetric matrix, then trace of $A$ is

Which of the following is always correct

If $\mathrm{A},\mathrm{ }\mathrm{B}$ are symmetric matrices of the same order then $\left(\mathrm{A}\mathrm{B}-\mathrm{B}\mathrm{A}\right)$ is -

If $A$ and $B$ are two skew-symmetric matrices of order $n$ , then

If $\mathrm{A}=\left[\begin{array}{lll}0& -1& 2\\ 1& 0& 3\\ -2& -3& 0\end{array}\right]$ , then $\mathrm{A}+2{\mathrm{A}}^{\mathrm{T}}$ equals -

If $A=\left[\begin{array}{ccc}6& 8& 5\\ 4& 2& 3\\ 9& 7& 1\end{array}\right]$ is the sum of a symmetric matrix $B$ and skew-symmetric matrix, $C$, then $B$ is

If $A$ is skew-symmetric matrix of order 3, then matrix $A^3$ is

If $A=\left[\begin{array}{c}6 8 5\\ 4 2 3\\ 9 7 1\end{array}\right]$is the sum of a symmetric matrix $B$ and skew-symmetric matrix $C$, then $B$ is

Let $A$ and $B$ be two symmetric matrices of same order. Then, the matrix $AB-BA$ is

If $A$ is a symmetric matrix and $n ϵ N$, then $A^n$is

If $A=\left[\begin{array}{c}6 8 5\\ 4 2 3\\ 9 7 1\end{array}\right]$is the sum of a symmetric matrix $B$ and skew-symmetric matrix $C$, then $B$ is