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**craig** Got a bit of a confusing problem involving matrices.

We assume that $\displaystyle (p,q,r)^T$ is a Pythagorean triple, so that $\displaystyle p^2 + q^2 = r^2$ where $\displaystyle p,q,r$ are positive integers.

For P,

$\displaystyle P = \left( \begin{array}{ccc} -1 & -2 & 2 \\ -2 & -1 & 2 \\ -2 & -2 & 3 \\ \end{array} \right)$.

Show that:

$\displaystyle P \left( \begin{array}{c} -p \\ q \\ r \\ \end{array} \right)$, $\displaystyle P \left( \begin{array}{c} p \\ -q \\ r \\ \end{array} \right)$ and $\displaystyle P \left( \begin{array}{c} -p \\ -q \\ r \\ \end{array} \right)$ are also Pythagorean triples.

Not sure where exactly to start here. Do I multiply them and then form some kind of equation, also a bit confused by the transposed bit at the start of the question?

Any points would be greatly appreciated :)

Thanks in advance