Shear transformations
A shear is a transformation of the plane that preserves straight lines and areas, but not angles.
A shear doesn’t move points along a line (its axis), and moves other points along lines parallel to the axis by an amount proportional to their distance from the axis (its shear factor).
The matrix of a shear whose axis is the x axis with shear factor a is 
, or
{{1,a},{0,1}} in GeoGebra code.
The reason areas are preserved come from Euclid: parallelograms on the same base and with the same height have the same area.