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.