If the system of equations

$$ \begin{aligned} &x+y+z=6 \\ &2 x+5 y+\alpha z=\beta \\ &x+2 y+3 z=14 \end{aligned} $$

has infinitely many solutions, then $$\alpha+\beta$$ is equal to

Let A and B be two $$3 \times 3$$ non-zero real matrices such that AB is a zero matrix. Then

Let $$\mathrm{A}$$ and $$\mathrm{B}$$ be any two $$3 \times 3$$ symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?

Let the matrix $$A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]$$ and the matrix $$B_{0}=A^{49}+2 A^{98}$$. If $$B_{n}=A d j\left(B_{n-1}\right)$$ for all $$n \geq 1$$, then $$\operatorname{det}\left(B_{4}\right)$$ is equal to :