Dpkg vs RPM:
rpm -qf /bin/ls dpkg --search /bin/ls
rpm -ql package dpkg -L package
rpm -e {package} dpkg -r {package}
rpm -i {file.rpm} dpkg -i {file.deb}
rpm -qa dpkg -l
More complicated commands I find useful are to list all packages by size on RPM and DEB distros respectively:
rpm -q -a --qf '%10{SIZE}\t%{NAME}\n' | sort -k1,1n
dpkg-query -W --showformat='${Installed-Size;10}\t${Package}\n' | sort -k1,1n
