Consider the following stress function,

$=a{x}^2{y}^3+b{x}^3{y}^2$

where a and $b$ are constants.

$($a$)$ Determine the $22($two$-$dimensional$)$ stress matrix, $.$

$($b$)$ Neglecting body forces, determine whether the stress function above satisfies the conditions of compatibility for a two$-$dimensional problem.