Is the following statement true ? If so, how is it proven ?

(1) Let

$\displaystyle f(x_1,\cdots,x_n) \in K[x_1,\cdots,x_n]$

is irreducible, where $\displaystyle K$ is a field.

Then it is still irreducible after any variable change

$\displaystyle

x_i=\phi_i(y_1,\cdots,y_m), \; i=1,\cdots,n.

$

(2) $\displaystyle K[x_1,\cdots,x_n]$ is not a principal ideal domain,

when $\displaystyle n \neq 1$.

Thank you in advance.