Originally Posted by

**mathportfolio99** Hi, so I have a pretty difficult question, at least for me:

Consider M =

[a+b.....a-b]

[a-b.....a+b]

Show that M = A + B, where A = aX and X=

[1 1]

[1 1]

and B bY and Y =

[1 -1]

[-1 1]

Then find a general expression for M^n in terms of aX and bY.

Test the validity of your general statement by using different values of a, b, and n. Discuss the scope and/or limitations of your general statement. Use an algebraic method to explain how you arrived at your general statement.

So, for my general statement I got M^n = a^nX^n + b^nY^n

I also have a feeling that n has to be a natural number..but I am not sure how to express why that is. Any help would be great!! Thanks!!