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**arze** $\displaystyle M=\left(\begin{array}{cc}a&b\\c&d\end{array}\right )$

$\displaystyle r_1=x_1i+y_1j$ and $\displaystyle r_2=x_2i+y_2j$ are any two vectors, and when multiplied by **M** they are transformed into $\displaystyle s_1$ and $\displaystyle s_2$ respectively. Given that *a,b,c,d* satisfy ab+cd=0 and $\displaystyle a^2+c^2=b^2+d^2$, show that the angle between $\displaystyle s_1$ and $\displaystyle s_2$ is the same as between $\displaystyle r_1$ and $\displaystyle r_2$.

If the two sets of vectors have the same angle between them the difference between the gradients would be the same, am I right?

Thanks