Answer Happy

Question is in Picture. This is from Abstract Algebra: Modules.
Please answer if you are familiar with the topic and can answer in
a clear and detailed way. The textbook used is: Abstract Algebra -
3rd Edition by David S. Dummit, Richard M. Foote. Thank you!
2. Fix n E N>2 and let R= Mn(F) for some field F. Let M be the subset of R with arbitrary elements of F in the first column and zeros elsewhere. Show that M is a submodule of R when R is considered as a left module over itself, but M is not a submodule of R when R is considered as a right module over itself.