# Matrix Multiplication

• Jan 12th 2011, 12:44 AM
seit
Matrix Multiplication
Find all symmetric 2x2 matrices A such that A^2 = 0.

thank you very much.
• Jan 12th 2011, 01:02 AM
Swlabr
Quote:

Originally Posted by seit
Find all symmetric 2x2 matrices A such that A^2 = 0.

thank you very much.

Where are you stuck with this problem?

There may be a more elegant solution, but I personally would just solve,

$\displaystyle \left( \begin{array}{cc} a & b \\ c & d \\ \end{array} \right)\left( \begin{array}{cc} e & f \\ g & h \\ \end{array} \right)= \left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \\ \end{array} \right)$

whilst remembering that either ad=bc or eh=gf (where did I get these from?).

You get 4 equations in 8 unknowns, but this doesn't actually matter because all it means is that your solutions won't be unique.

(That is, there is more than one possible solution to your equations. For example, a=b=c=d=0, all the others whatever, and a=b=c=0, d=1=e,, f=g=h=0 are two different solutions.)
• Jan 12th 2011, 03:17 AM
DrSteve
You can solve this matrix equation:

$\displaystyle \left( \begin{array}{cc} a & b \\ b & d \\ \end{array} \right)\left( \begin{array}{cc} a & b \\ b & d \\ \end{array} \right)= \left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \\ \end{array} \right)$
• Jan 12th 2011, 03:39 AM
seit
Thanks so much. I have done this exercise.