Moment of inertia of a square plate of side l about the axis...

Use parallel axis theorem to get the magnitude of the moment of inertia of a square plate of side $l$ about the axis passing through one of the corners and perpendicular to the plane of a square plate,

${I}_{z} = {I}_{cm} + M{\left(\dfrac{l}{\sqrt{2}}\right)}^{2}$

$⇒ {I}_{z} = \dfrac{M{l}^{2}}{6} + \dfrac{M{l}^{2}}{2} = \dfrac{4M{l}^{2}}{6} = \dfrac{2M{l}^{2}}{3}$.