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are counterexamples to the converse.

Shear mapping takes a rectangle to a parallelogram of the same area. Written in matrix form, a shear mapping along the -axis is
:

Squeeze mapping lengthens and contracts the sides of a rectangle in a reciprocal manner so that the area is preserved. Written in matrix form, with λ > 1 the squeeze reads
:

A linear transformation multiplies areas by the absolute value of its determinant

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