Question

Malevolence19,
Are the only matrices that have this property:
A^2 = A
the identity matrix and the 0 matrix?

Answer 1

amistre64 told me you are pretty good at this..

Answer 2

anybody?

Answer 3

Yes. Given either of those you have:
\[\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]*\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]=\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]\]
However, if you try anything else It falls apart because once you multiply row by column you have to add them. So if you tried like:
\[\left[\begin{matrix}1 & 1\\ 1 & 1\end{matrix}\right]*\left[\begin{matrix}1 & 1\\ 1 & 1\end{matrix}\right]=\left[\begin{matrix}2 & 2\\ 2 & 2\end{matrix}\right]\]
So, as far as I know, only the zero matrix and identity hold this property.

Answer 4

http://home.scarlet.be/~ping1339/matr.htm#Multiplication-of-tw
deals with multiplication of matrices

Answer 5

jimmyrep, i know how to multiply matrices as long as a person knows how to multiply and add everyone can multiply and add matrices....
And malevolence thanks.. this was for the proofs, I can prove this one now, but I have a couple that I can't.. Determine which of the following subsets of R^(nxn) are in fact subspaces of R^(nxn)
c) The nonsingular matrices
d) The singular matrices
g) All matrices that commute with the given matrix A
i) All matrices such that trace(A)=0

Answer 6

bahrom7893 - don't suggest for 1 minute that you dont know how to multiply matrices and i'm sorry if you thought i did.
this website goes into it in detail and if you look at it it deals with you question with regard to matrices with the property A = A^2 - there are more than just unit and zero

Answer 7

my first sentence should start 'bahrom7893 - I don't'

Answer 8

Sorry man I didn't read the link carefully.. yea, malevolence was wrong.. Not only 0 and I matrices hold that property, there are more.. they are called idempotent matrices

Answer 9

I'm sorry D;