S.O.S. Mathematics CyberBoard

the matrix A is a 3x3 that looks like...
5 -3 2
15 -9 6
10 -6 4

I am supposed to find A^2 ..when i square A I get zeros in all of the spots. Am i supposed to be getting this answer? When you square a square matrix is it always zeros or is this just a special problem?

You should try squaring ANY OTHER MATRIX, and you'll most likely get a different answer from 0. Heck, try squaring the IDENTITY MATRIX. If ever you have a question like this, you should try some other examples to see if it's true then. That's the easiest way to figure out most of these kinds of questions.

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Hello, lauren72!

Two reasons this happened:

(1) When you row reduce your given matrix, you get two rows of zeros in the row reduced echleon form...

and

(2) Attempt to diagonalize it (if you know how to do it). You will get an interesting eigenvalue!

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"Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another." Bernard Le Bovier Fontenelle (1657-1757)

"In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy."
G.H. Hardy (1877-1947)