ABAB versus BABA.

Maya is really perfecting mumbling things like MMBA, ABA, BABABA, it is very sweet.
Which brings me to this question: Let A and B be two square matrices of same size, if ABAB=0, does this imply that BABA=0?

Time to submerge.

52 'weeks' of math.

We have reached week 52  in our math project: https://sites.google.com/site/77neuronsprojectperelman/weeks/week51-matrix-inverses

To celebrate, I wish to thank Lena one billion times for tolerating this endeavor, and I invite anybody reading to prove this:

Prove that for any 2x2 matrix T, you can always find numbers c0,c1,c2,c3,c4 at least one of which not equal to zero, such that:c4.T^4+c3.T^3+c2.T^2+c1.T+c0.I=Z.

I is the identity matrix, and Z is the zero matrix.
T^n is T multiplied by itself n times.