Do you know how to multiply matrices?
If you don't know that then there is no point of doing anything else.
Do you know the methods of calculating inverse of a matrix by hand?

>>127720
Yeah, it took a while, but I got the second and third questions (i think).
Number 4 still confuses me, but only because I dont exactly know the solution method to that particular question.

>>127730
Try multiplying row consisting of 0s by a nonzero column?

>>127732
been stuck for a while now, can you maybe give a little more insight?

>>127752
m-th row of matrix AB will consist of 0s. Why? Because the m-th row is achieved by multiplying the m-th row of A by every column of B.
0*anything=0

>>127756
So given I create a case for that to be true, how do I make a proof by induction for that?

>>127770
>So given I create a case for that to be true
what

Why do you want to use induction

>>127772
In class the teacher always wants us to prove everything.
The question only asks for one case, which given your advice makes sense! (Thanks again), but I think I need a more abstract proof, abstract may be the wrong word. I can prove that AB will have a row of zeros, but that's only one case

>>127774
Question asks for a general case of finite matrices that can be multiplied. Nothing I said relates to some specific scenario. What other cases?
Not every proof is made by induction.

>>127778
Sorry, this is the first class that emphasized proofs, so I'm terrible with the syntax

>>127786
You still need that proof written formally or can you do it yourself.

>>127789
I think I can do it, thanks again dude. This class is just really difficult for me, all the kids in there are computer science majors and have been doing this as a hobby for ages so I hate asking questions