If you used the Nano SD card image, then yes, it already has the CUDA Toolkit installed. Check under /usr/local/cuda
to verify that it’s there.
Check that your ~/.bashrc
file has these lines at the end, and if not, add them and restart your terminal:
$ export PATH=/usr/local/cuda/bin${PATH:+:${PATH}}
$ export LD_LIBRARY_PATH=/usr/local/cuda/lib64\
${LD_LIBRARY_PATH:+:${LD_LIBRARY_PATH}}