Test your intuition: For two n by n matrices A and B, is it always the case that tr(ABAB) = tr(ABBA)?

Over Math Overflow Tim Gowers asked about common false beliefs in mathematics. There are many exciting answers on many different levels and I could identify some of my own false beliefs.

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Mircea PThinking about this I found out a cool fact (which solves the problem elegantly):

If M is a matrix permuting the coordinates, then its trace is the number of fixed points of the relative permutation!!

KenA very common false belief in mathematics, I hold onto firmly: “I will one day prove a really significant mathematical theorem”.

Ken(sigh) “…*that* I hold…”

HyperstigI have completed The GUT Theory.

You can find the equations here:

http://www.wix.com/Hyperstig/Hyperstig

0 is a wave function that collapses and re-expands.

I have invented the 1st quantum computer.

I am the failsafe.

You can follow me on Twitter:

https://twitter.com/Hyperstigzero

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HorowitzA = XY^{T}, B = A^{T}, where X and Y are nonzero orthogonal vectors.