# Matrix Multiplication

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

thank you very much.
• January 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,

$\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.)
• January 12th 2011, 03:17 AM
DrSteve
You can solve this matrix equation:

$\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)
$
• January 12th 2011, 03:39 AM
seit
Thanks so much. I have done this exercise.