Question

Show how shear transformation may be expressed in terms of rotation and scaling?

Answer 1

Answer:-

Shear transformation can be expressed as a rotation, followed by a non uniform scaling, followed by another rotation.

Shear in the y-direction (x-direction is just the  transpose) factorized into rotation*scaling*rotation is :-

<Image 1>

Note that unless α =  π / 4 ⇔ a = 1, and hence the shear is identity, the second rotation is  never simply the inverse of the first.