Let $f(r,\theta)=(r\cos\theta ,r\sin\theta)$ for $(r,\theta)$ $\in \mathbb R^2$ with $r\ne0$. then which are true statements?
$1$.$Df(r,\theta)$ is not zero for any $(r,\theta)$ with $r\ne0$
$2$.$Df(r,\theta)=r^2I$ for any $(r,\theta)$ with $r\ne0$
here $Df(r,\theta)$ is the matrix $\begin{bmatrix} \cos\theta &-r \sin\theta \\ \sin\theta & r\cos\theta \end{bmatrix}$.its determinant is $r$ which is nonzero.so $1$ true.but what about $2$?
Can anyone help me please .