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

If $A$ is a symmetric matrix,then the matrix $M'AM$ is

Let $A + 2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix}$ and $2A - B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix}$. Then $Tr(A) - Tr(B)$ has the value equal to:

If $A'$ and $B'$ are the transpose matrices of the square matrices $A$ and $B$ respectively,then $(AB)'$ is equal to:

Show that the matrix $A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix}$ is a skew-symmetric matrix.

If a square matrix $A$ is such that $\left(A^T-\frac{1}{2} I\right)\left(A-\frac{1}{2} I\right) = \left(A^T+\frac{1}{2} I\right)\left(A+\frac{1}{2} I\right) = I$,where $I$ is a unit matrix,then $A$ is