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Matrix Reflection and Rotation Problems

Given the 2x2 matrices A, B, and C (active transformation matrices) in the x, y plane do the following:
(A, B and C are 2x2 matrices given below)

1. Show the matrix is orthogonal

2. Find the determinant to indicate if a rotation or reflection matrix

3. Find the rotation angle or find the line of reflection.

A= 1/(2)^.5 [(1,1),(-1,1)] B=[(0.-1),(-1,0)] C= 1/(2)^.5 [(-1,1),(1,-1)]

What is important are clear detailed methodology descriptions for the solution method that can be used generally by students.

Solution Summary

Matrix reflection and rotation are investigated in this solution, which is given in two Word files and uses calculation to solve the problems.