Symmetric and Skew-symmetric Matrices

Express the square matrix $A$ as the sum of a symmetric and a skew-symmetric matrix.

$P=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$ and $Q=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$ are equal matrices.

Which one is an example of Symmetric Matrix ?

What is Skew Symmetric Matrix ?

What is Symmetric Matrix?

What is row matrix? Give two example of row matrix.

If $A$ is a square matrix then $\left(A+A^{\text{'}}\right)$ is

$A$ and $B$ are square matrices of same order, prove that:

If $A, B \text{and} AB$ are all symmetric, then $AB-BA=0$.

If the matrix $A=\left[\begin{array}{ccc}0& -2& -3\\ 2& 0& -1\\ a& 1& 0\end{array}\right]$  is skew symmetric then find the value of $a$.

If the matrix $A=\left[\begin{array}{ccc}0& a& -3\\ 2& 0& -1\\ 3& 1& 0\end{array}\right]$  is skew symmetric then find the value of $a$.

If $\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]$ is a symmetric matrix, then find the value of $x$.

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