if [ -4 5 -2 5/2] find a non-zero 2 by 2 zero matrix X, such that A.X=O_2x2

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if [ -4 5 -2 5/2] find a non-zero 2 by 2 zero matrix X, such that A.X=O_2x2

Mathematics
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is O spose to be anything special? other than a 2x2 matrix?
and I take it the given matrix is A:
\[\left[\begin{matrix}-4 & 5 \\ -2 & 5/2\end{matrix}\right]\]

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find a nonzero, zero matrix?
A.X = 0 is what i think im reading, such that X is not a 0
so they need to be orthogonal at best
\[z_{11}=-4x_{11}+5x_{21}=0\] \[z_{21}=-2x_{11}+\frac{5}{2}x_{21}=0\] \[z_{12}=-4x_{12}+5x_{22}=0\] \[z_{22}=-2x_{12}+\frac{5}{2}_{22}=0\] would be our corresponding equations maybe
A.X= to the letter O and not 0
the name is unimportant methinks, but its spose to zero out
-4x + 5y = 0 4x - 5y = 0 ----------- i dont thinks its doable but i could be wrong
detA = 0 so its dependant for starters, i think that throws a monkeywrench in the plans
or maybe, since its just one vector, we can flip and negate the entries to get a perp vector; hmmm \[\begin{pmatrix}-4&5\\-2&\frac{5}{2}\end{pmatrix}.\begin{pmatrix}2&-\frac{5}{2}\\-4&5\end{pmatrix}\] maybe?
that doesnt work either
i was on the right track :)
http://www.wolframalpha.com/input/?i=%7B%7B-4%2C5%7D%2C%7B-2%2C5%2F2%7D%7D.%7B%7B-5%2C-5%2F2%7D%2C%7B-4%2C-2%7D%7D this one!! lol

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