If $A=\left[\begin{array}{ll}\frac{1}{\sqrt{5}}& \frac{2}{\sqrt{5}}\\ \frac{-2}{\sqrt{5}}& \frac{1}{\sqrt{5}}\end{array}\right],B=\left[\begin{array}{ll}1& 0\\ i& 1\end{array}\right],i=\sqrt{-1}$, and $Q=A^{T}BA$, then the inverse of the matrix $A{Q}^{2021}{A}^{\mathrm{T}}$ is equal to:

Two fair dice are thrown. The numbers on them are taken as $\mathrm{\lambda }$ and $\mathrm{\mu },$ and a system of linear equations
$x+y+z=5$

$x+2y+3z=\mu$

$x+3y+\lambda z=1$
is constructed. If $p$ is the probability that the system has a unique solution and $q$ is the probability that the system has no solution, then:

If the system of linear equations

$2x+y-z=3$

$x-y-z=\alpha$

$3x+3y+\beta z=3$

has infinitely many solutions, then $\left|\alpha +\beta -\alpha \beta \right|$ is equal to __________.