Determine if the statements below are True or False. If it’s True, explain why. If it’s False explain why not, or simply give an example demonstrating why it’s false If T : R2 → R2 is a linear...

Determine if the statements below are True or False.
If it’s True, explain why. If it’s False explain why not, or simply give an example
demonstrating why it’s false

If T : R2 → R2
is a linear transformation given by counter-clockwise rotation
around the origin by some angle θ, then T either has no (real) eigenvalues, or it
has eigenvalue 1 (only).