Let A be an nxn matrix and consider the linear homogeneous system Ar= 0. If the linear system has only the trivial solution

Question

Let A be an nxn matrix and consider the linear homogeneous system Ar= 0. If the linear system has only the trivial solution state whether the following statements are true or false.
(a) 0 is an eigenvalue of A
(b) All columns of A are basic columns.
(c) Rank of A is n.

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