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Matrix Reflection and Rotation Problems

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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.

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

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

1. show the matrix is orthogonal
A matrix A is an orthogonal matrix if , where is the transpose of A and I is the identity matrix.

So matrix A is orthogonal.

B ...

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