The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:

If $A = \begin{bmatrix} 0 & 5 \\ 0 & 0 \end{bmatrix}$ and $f(x) = x + x^2 + \dots + x^{2018}$, then $f(A) + I =$

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation $AA^T = 9I$,where $I$ is the $3 \times 3$ identity matrix,then the ordered pair $(a, b)$ is equal to:

If $A = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}$ and $A^3 = \begin{bmatrix} \cos 3 \theta & m \\ n & \cos 3 \theta \end{bmatrix}$,the values of $m$ and $n$ respectively are

If $A = \begin{bmatrix} a & b \\ b & a \end{bmatrix}$ and $A^2 = \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \end{bmatrix}$,then:

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 5 & 0 & 7 \\ 6 & 2 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 & 5 \\ 0 & 0 & 2 \end{bmatrix}$,then which of the following is defined?