Question-91

Which of these statements are true with respect to square matrices of order \(\displaystyle 2\)?

• Every orthogonal matrix is a rotation matrix.
• Every rotation matrix is an orthogonal matrix.
• Every reflection matrix is an orthogonal matrix.
• Every orthogonal matrix is a reflection matrix.

Answer

• Every orthogonal matrix is a rotation matrix.
• Every rotation matrix is an orthogonal matrix.
• Every reflection matrix is an orthogonal matrix.
• Every orthogonal matrix is a reflection matrix.

Solution

Rotation and reflection and matrices are orthogonal matrices. An orthogonal matrix need not be a pure reflection or rotation. In general, it is a combination of rotation and reflection matrices.