The matrix M =
[−3/5 4/5]
[4/5 3/5]
defines an isometry of the xy-plane.
(a)What special properties do the column vectors of this matrix have?
(b)Verify that the point (2, 4) remains stationary when M is applied to it.
(c)What is the significance of the stationary point (2, 4)? What does it tell you about the possible isometries that M could be? Do other points invite examination?
(d)Show that MM is the 2×2 identity matrix. What does this suggest about the geometric transformation that M represents? Confirm your suspicions.