$A$ 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 $A$ and $B$ are square matrices of order $n$ such that $A^{2}-B^{2}=(A-B)(A+B)$,then which of the following will be true?

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

If $A = \begin{bmatrix} 2 & 2 \\ -3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then $(B^{-1}A^{-1})^{-1} = $

If $A = \begin{bmatrix} 0 & 1 & 2 \\ 2 & 3 & 0 \\ 4 & 0 & 3 \end{bmatrix}$ and $B$ is a matrix such that $AB = BA$. If $AB$ is not an identity matrix,then the matrix that can be taken as $B$ is:

If $A = \begin{bmatrix} \lambda & 1 \\ -1 & -\lambda \end{bmatrix}$,then for what value of $\lambda$ is $A^2 = O$?