While checking online for the conversion of co-ordinate systems, i came across two similar but different matrix form for converting spherical to Cartesian. So which one is correct or are they both the same?
$$\begin{align}\begin{bmatrix}A_R\\A_{\theta}\\A_{\phi}\end{bmatrix}&=\begin{bmatrix}\sin\theta\cos\phi&\cos\theta\cos\phi&-\sin\phi\\\sin\theta\sin\phi&\cos\theta\sin\phi&\cos\phi\\\cos\theta&-\sin\phi&0\end{bmatrix}^{-1}\begin{bmatrix}A_x\\A_y\\A_z\end{bmatrix}\\&=\begin{bmatrix}\sin\theta\cos\phi&\sin\theta\sin\phi&\cos\theta\\\cos\theta\cos\phi&\cos\theta\sin\phi&-\sin\theta\\-\sin\phi&\cos\phi&0\end{bmatrix}\begin{bmatrix}A_x\\A_y\\A_z\end{bmatrix}\end{align}$$
or
$$\begin{align}\begin{bmatrix}A_R\\A_{\theta}\\A_{\phi}\end{bmatrix}&=\begin{bmatrix}\sin\theta\cos\phi&\sin\theta\sin\phi&\cos\theta\\-\cos\theta\cos\phi&\cos\theta\sin\phi&-\sin\theta\\-\sin\phi&\cos\phi&0\end{bmatrix}\begin{bmatrix}A_x\\A_y\\A_z\end{bmatrix}\\\begin{bmatrix}A_x\\A_y\\A_z\end{bmatrix}&=\begin{bmatrix}\sin\theta\cos\phi&\cos\theta\cos\phi&-\sin\phi\\\sin\theta\sin\phi&\cos\theta\sin\phi&\cos\phi\\\cos\theta&-\sin\phi&0\end{bmatrix}\begin{bmatrix}A_R\\A_{\theta}\\A_{\phi}\end{bmatrix}\end{align}$$