rustup gives command not found error with zsh even after installing with brew

I used the following steps to install Rust on MacOS:

1. Install Rust using:

   curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh
   

   Make sure that you customize the installation and answer No when it asks to modify the Path.

2. Once successfully done, then add the Path variable to .zshrc using:

   • To open .zshrc use nano ~/.zshrc
   • Add export PATH="$HOME/.cargo/bin:$PATH" to .zshrc

3. Check if the installation was successfull using rustc --version
   If that doesn’t work right away then use the command:
   source $HOME/.cargo/env and rerun rustc --version.