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:

Let $2A+B = \begin{bmatrix} 1 & 0 & 3 \\ -1 & 4 & 6 \\ 2 & 5 & 2 \end{bmatrix}$ and $A-2B = \begin{bmatrix} 2 & -1 & 5 \\ 0 & 3 & 6 \\ 1 & 2 & 1 \end{bmatrix}$. Then $Tr(A) - Tr(B)$ has the value equal to (where $Tr(A)$ denotes the trace of matrix $A$).

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

Which of the following is an orthogonal matrix?

If $A = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}$,then $A \cdot A^{\prime}$ is

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