If $A$ and $B$ are square matrices of order $3 \times 3$,$A$ is non-singular,and $AB = O$,then $B$ is a:

The matrix $A = \frac{1}{3}\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ -2 & 2 & -1 \end{bmatrix}$ is

If $A$ and $B$ are square matrices of the same order such that $AB = BA$,then prove by induction that $AB^{n} = B^{n}A$. Further,prove that $(AB)^{n} = A^{n}B^{n}$ for all $n \in N$.

If $A = \frac{1}{2} \begin{bmatrix} 1 & \sqrt{3} \\ -\sqrt{3} & 1 \end{bmatrix}$,then :

$A$ row matrix has only

If $A = \begin{bmatrix} 1 & 2 & 3 \\ -2 & 3 & -1 \\ 3 & 1 & 2 \end{bmatrix}$ and $I$ is a unit matrix of $3^{rd}$ order,then $(A^2 + 9I)$ equals