Symmetric and Skew - symmetric Matrices

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

If $A=\left[\begin{array}{ccc}-2& -1& 1\\ -1& 7& 4\\ 1& -x& -3\end{array}\right]$ is a symmetric matrix then the value of $x$ is _____.

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

If $x, y$ are any two non-zero real numbers, $a_{ij}=xj+yi,A={\left(a_{ij}\right)}_{n\times n}$ and $P, Q$ are two $n\times n$ matrices such that $A=x P+y Q$ then

Determinant of skew-symmetric matrix of order "three" is always

If $A=\left[\begin{array}{ccc}-2& -1& 1\\ -1& 7& 4\\ 1& -x& -3\end{array}\right]$ is a symmetric matrix then find the value of $x$.

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 $A{A}^T$ and $A^{T}A$ are symmetric matrix.

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 a skew-symmetric matrix.

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 $A=\left[\begin{array}{cc}6& 2\\ 5& 4\end{array}\right]$

If $A$ and $B$ are two skew symmetric matrices of same order, then $AB$ is symmetric matrix if _____

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 matrix $\mathrm{A}$ is both symmetric and skew symmetric then

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

If $\mathrm{A}=\left[\begin{array}{ccc}\mathrm{x}& 3& 2\\ -3& \mathrm{y}& -7\\ -2& 7& 0\end{array}\right]\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }\mathrm{A}=-{\mathrm{A}}^{\mathrm{\prime }},\mathrm{ }\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}\mathrm{ }\mathrm{x}+\mathrm{y}\mathrm{ }$ is equal to

The symmetric part of the matrix $A=\left[\begin{array}{ccc}1& 2& 4\\ 6& 8& 2\\ 2& -2& 7\end{array}\right]$ 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

In a symmetric matrix of order $\mathrm{‘}12\mathrm{’}$ maximum number of distinct elements are -