Since I’m on Wayland, the best way to install Matlab should be mpm.
The Wiki page worked for me and the steps I executed include:

yay matlab-mpm
mpm install --release=R2025b --destination=~/matlab MATLAB 
#ofc, you can change the destination

Normally, you should be able to just execute ~/matlab/bin/glnxa64/MathWorksProductAuthorizer.sh and finish activating your license. However it didn’t went that smooth for me, because recent gnutls update (likely 3.8.10-1 or newer) breaks the TLS handshake in MATLAB’s bundled licensing libraries (libmwinstall\_activationwsclientimpl.so and libmwlmgrimpl.so), causing the segfault when the tool tries to connect to MathWorks servers.
So I ran these to make Matlab use the old version of gnutls :

wget https://archive.archlinux.org/packages/g/gnutls/gnutls-3.8.9-1-x86_64.pkg.tar.zst
mkdir -p matlab/gnutls
tar -xf gnutls-3.8.9-1-x86_64.pkg.tar.zst -C matlab/gnutls
mkdir -p ~/matlab/bin/glnxa64/gnutls
cp -a ~/matlab/gnutls/usr/lib/libgnutls* ~/matlab/bin/glnxa64/gnutls/
cd /home/user/matlab/bin/glnxa64/
ln -s gnutls/* ./

And that should be fine. Now you can continue to run ~/matlab/bin/glnxa64/MathWorksProductAuthorizer.sh, finishing setup and launch.
To launch Matlab faster from terminal you can add this line in .bashrc:

alias matlab='/home/user/matlab/bin/matlab' #change it to the path the executable locates

Or, alternatively, make a desktop entry with sudo nano /usr/share/applications/matlab.desktop:

[Desktop Entry]
Type=Application
Terminal=false
MimeType=text/x-matlab
Exec=/home/user/matlab/bin/matlab -desktop -useStartupFolderPref
Name=MATLAB
Icon=matlab
Categories=Development;Math;Science
Comment=Scientific computing environment
StartupNotify=true