Quick math question

On the small chance that there is someone on this forum that is my mathematical equal or superior, assuming A is a 2x2 matrix how mnay different matricies exist such that A^2=I ?

 

Is this just a test to see if someone is close to you? I think FlyingTiger or Nikzad would be the ppl close to you LK.

 

No, not test I just can't seem to think outside the box atm was hoping someone had some insight.

P.S. If this was a test I would ask about linear trnaformations, kernels, and ranges. I just know there are a few college level students here and maybe one of them took a high level linear algebra class recently.

 

Yea well I did pretty good back in high school, but then started to skip so I failed classes after a certain point.

 

Psh. I remember doing stuff like that so easily.

Once my math teacher gave us a 4X4 Matrix to break down into it's simplest forms.

Using the traditional method. So no shortcuts.

I used 3 sheets of paper to solve the thing.

Anyways...



I would say that there is only 1 solution. If "A" is equal to "I," then squaring that matrix would result in the same number, which means that A would still be equal to I.

But squaring any other matrix couldn't equal "I" (at least I think so, I'm a bit rusty at Algebra) because A ^ -1 equals I. And if you were to change the exponent then the matrix couldn't equal I.

So I only see 1 solution. But if I'm wrong (there's a good chance of that), then there's an infinite number of solutions.

 

LK, stumped on a math question?

My mind, she is blown.

 

I am 99% sure the answer is 4 but after putting that down as an answer with supporting evidence I was marked wrong (or atleast not fully correct) so I am stumped as to where to jump and whether or not the grader may have just messed up.

The only method I havn't tried that I can think of would take an inordinate amount of time and killed my calculator when I tried to make it do a version of it in the passed. So I was just hoping that someone who had done the problem (or a version of it) recently, may have some insight.

P.S. Fenix it is not so much that I am stumped such that I don't want to accuse my professor of incompetence until I am sure.

 

I have my answer. I am an idiot. Topic locked.