Thread: Theoretical questions on determinants (I have the answers, I just want explanations)

The correct answers are AF, BCD, and BC. Sorry if this sounds demanding but could someone go through them for me and explain why or why not each line is true or false? (If you're too lazy, you can give me a half-answer and leave the rest to be completed by someone else).

Any explanation would be greatly appreciated!
Thanks in advance!

If M has nonzero determinant, it is invertible. Thus the equation may be written as

.

Clearly, then, any A will immediately correspond to a unique X.