9. Which of the following statements are true and which are false? Justify your answer with
a short proof or a counterexample. (10)
I) R² has infinitely many non-zero, proper vector subspaces.
ii) If T : V →W is a one-one linear transformation between two finite dimensional
vector spacesV and W then T is invertible.
iii) If A^k = 0 for a square matrix A, then all the eigenvalues of A are zero.
iv) Every unitary operator is invertible.
v) Every system of homogeneous linear equations has a non-zero solution.

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