For any square matrix $A$,$AA^T$ is a

If $A$ is a square matrix,then which of the following matrices is not symmetric?

If $A$ and $B$ are symmetric matrices of the same order such that $AB+BA=X$ and $AB-BA=Y$,then $(XY)^{T}=$

Let $A+2 B=\left[\begin{array}{ccc}1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1\end{array}\right]$ and $2 A - B =\left[\begin{array}{ccc}2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2\end{array}\right] .$ If $\operatorname{Tr}( A )$ denotes the sum of all diagonal elements of the matrix $A ,$ then $\operatorname{Tr}( A )-\operatorname{Tr}( B )$ has value equal to

If the matrix $\begin{bmatrix} a & 2 & -3 \\ b & 0 & 4 \\ c & -4 & 0 \end{bmatrix}$ is a skew-symmetric matrix,then $a+b+c=$

Which of the following relations regarding the transpose of a matrix is incorrect?