$12\mathrm{.}1.$ Find the critical buckling load, $N_{x_{cr}}$ in lbs$./$in$.$ for a plate simply supported on all four edges made of a material whose flexural stiffness properties are given as follows and whose thickness is $1$ inch.

$[D]\left[\begin{array}{ccc}1\mathrm{.}63& 0\mathrm{.}028& 0\\ 0\mathrm{.}028& 0\mathrm{.}160& 0\\ 0& 0& 0\mathrm{.}037\end{array}\right]{10}^{6}lb.-in.$

$($a$)$ If $a=30$ inches and $b=20$ inches.

$($b$)$ If $a=50$ inches and $b=12$ inches.Please answer it clearly and do not use chatgpt