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## 'Square Pair' printed from http://nrich.maths.org/

A 2D constant matrix $M$ acts on the plane, transforming each point
with position vector ${\bf r}$ to another point with position
vector $M{\bf r}$.

A particular square $S$ has corners with coordinates
$(0,0), (0,1), (1,0), (1,1)$.

The action of the matrix $M$ on the points making up the square $S$
produces another shape in the plane.

What quadrilaterals can I transform $S$ into?

What quadrilaterals can I not transform $S$ into?

What shapes other than quadrilaterals can I transform $S$
into?

Another square $T$ has coordinates $(4,4), (6, 2), (8, 4), (6,
6)$.

When will $S$ and $T$ transform into the same type of
quadrilateral? When will they transform into two different
types of quadrilateral? Construct the matrices $M$ in
each case.