$A$ square matrix $[a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a

If $A=\begin{bmatrix} 1 & 1 \\ 0 & i \end{bmatrix}$ and $A^{2018}=\begin{bmatrix} a & b \\ c & d \end{bmatrix}$, then $(a+d)$ equals

If $m[-3, 4] + n[4, -3] = [10, -11]$, then $3m + 7n$ is equal to

Let $A = [a_{ij}]$ be a real matrix of order $3 \times 3$,such that $a_{i1} + a_{i2} + a_{i3} = 1$,for $i = 1, 2, 3$. Then,the sum of all the entries of the matrix $A^3$ is equal to:

Construct a $2 \times 2$ matrix,$A = [a_{ij}]$,whose elements are given by $a_{ij} = \frac{i}{j}$.

Let the matrix $A = \begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}$ satisfy $A^n = A^{n-2} + A^2 - I$ for $n \geq 3$. Then the sum of all the elements of $A^{50}$ is: