If $A$ is a symmetric matrix and $B$ is skew- symmetric matrix such that $A+B=\left[\begin{array}{cc}2& 3\\ 5& -1\end{array}\right]$ , then $AB$ is equal to:

An ordered pair $\left(\alpha , \beta \right)$ for which the system of linear equations
$\left(1+\alpha \right)x+\beta y+z=2$
$\alpha x+\left(1+\beta \right)y+z=3$
$\alpha x+\beta y+2z=2$

has a unique solution, is :

If the system of linear equations

$x+ky+3z=0$
$3x+ky-2z=0$
$2x+4y-3z=0$

has a non-zero solution $\left(x, y, z\right),$ then $\frac{xz}{y^2}$ is equal to: