Some commands in Sage are “functions,” an example is factorial() above. Other commands are “methods” of an object and are like characteristics of objects, an example is .inverse() as a method of a matrix. Once you know how to create an object (such as a matrix), then it is easy to see all the available methods. Write the name of the object, place a period (“dot”) and hit the TAB key. If you have A defined from above, then the compute cell below is ready to go, click into it and then hit TAB (not “evaluate”!). You should get a long list of possible methods.
To get some help on how to use a method with an object, write its name after a dot (with no parentheses) and then use a question-mark and hit TAB. (Hit the escape key “ESC” to remove the list, or click on the text for a method.)
With one more question-mark and a TAB you can see the actual computer instructions that were programmed into Sage to make the method work, once you scoll down past the documentation delimited by the triple quotes ("""):
It is worthwhile to see what Sage does when there is an error. You will probably see a lot of these at first, and initially they will be a bit intimidating. But with time, you will learn how to use them effectively and you will also become more proficient with Sage and see them less often. Execute the compute cell below, it asks for the inverse of a matrix that has no inverse. Then reread the commentary.
Click just to the left of the error message to expand it fully (another click hides it totally, and a third click brings back the abbreviated form). Read the bottom of an error message first, it is your best explanation. Here a ZeroDivisionError is not 100% accurate, but is close. The matrix is not invertible, not dissimilar to how we cannot divide scalars by zero. The remainder of the message begins at the top showing were the error first happened in your code and then the various places where intermediate functions were called, until the actual piece of Sage where the problem occurred. Sometimes this information will give you some clues, sometimes it is totally undecipherable. So do not let it scare you if it seems mysterious, but do remember to always read the last line first, then go back and read the first few lines for something that looks like your code.