A cardinal $\kappa$ is weakly inaccessible iff $\kappa > \omega$, $\kappa$ is regular, and $\forall\lambda<\kappa(\lambda^+<\kappa)$

(here $\lambda^+$ is the successor cardinal)

A cardinal $\kappa$ is strongly inaccessible iff $\kappa > \omega$, $\kappa$ is regular, and $\forall\lambda<\kappa(2^\lambda<\kappa)$

My question is how to prove if $\kappa$ is weakly inaccessible, then it is the $\kappa$-th $\aleph$ fixed point, also if $\kappa$ is strongly inaccessible, then it is the $\kappa$-th $\beth$ fixed point?

This question is found in I.13.17 of The Foundations of Mathematics by Kenneth Kunen.