Precisely one of the four matrices specified below is not orthogonal. Which is it?
Give a brief justification.
Given that the four matrices represent transformations of corresponding (in no particular order) to a rotation, a reflection, a combination of a rotation and a reflection, and none of these, identify each matrix. Explain your reasoning.
[Hint: For two of the matrices, and say, you may find it helpful to calculate and , where is the identity matrix.]