## Matrix Multiplication

1. The problem statement, all variables and given/known data

I can't figure out how to latexa 3X3 matrix so here's my ghetto method

A =
0 0 -1
0 2 0
0 0 1

What is

2. Relevant equations

I'm trying to find $$A^{7}$$

3. The attempt at a solution

I'm assuming there's some type of shortcut to get this... So I did a squared and then multipled a squared times a squared to get a to the fourth... I was about to multiply A times a squared and then that times a to the fourth but I didn't think that was ok to do since multiplication isn't commutative and I don't know which order to multiply... Is my method ok? Any other suggestions?

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 you should look for which numbers stay the same regardless of the number of times you multiply it. There are some other elements that stay the same. Which?

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 Quote by robbondo I didn't think that was ok to do since multiplication isn't commutative
In general it's not... but can you prove that it is in this case?

 I don't know which order to multiply...
What does the definition of exponentiation say?

## Matrix Multiplication

Oops I screwed up on the original posting...

so the matrix is

0 0 -1
0 2 0
2 0 0

And I don't really see any repetition at all which was what I was hoping would happen... For A squared I got

-2 0 0
0 4 0
0 0 -2

Then for A^4 I get

4 0 0
0 16 0
0 0 4

So there's no really observable pattern that I can see except for the fact that A^2 and A^4 so A^4 is all the values from A^2 squared... But now when I go to start multiplying things that aren't the same I don't know which order to do it in...

 I don't know what the deff. of exponentiation is... Exponentiation for matrix's or in general? This is the very beginning of my lin alg class...

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 Quote by robbondo I don't know what the deff. of exponentiation is... Exponentiation for matrix's or in general? This is the very beginning of my lin alg class...
Exponentiation for matrices. Your text should either precisely explain the order of operations, or indicate why the order shouldn't matter. (And if it doesn't, it ought to. )

The order, in fact, doesn't matter -- and I think it would be a good exercise for you to try and figure out why. Start with an easy case -- e.g. show that

M(MM) = (MM)M

for any square matrix M.

 In general. Well, for nonnegative integer exponents anyway.
 I guess that makes sense since it's the same matrix. My sucky book doesn't have anything under exponentiation in the index but it may be in there, just not in the beginning sections were in right now. Thanks for the help, I finished the problem.
 Recognitions: Gold Member Science Advisor Staff Emeritus Your "sucky" book probably assumed that you had taken basic algebra, at least enough to know what "exponentiation" meant, before taking linear algebra.

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