Question: Let A be an n n matrix. (a) Show that A2 = 0 if and only if col A null A. (b) Conclude

Let A be an n × n matrix.
(a) Show that A2 = 0 if and only if col A ⊆ null A.
(b) Conclude that if A2 = 0, then rank A ≤ n/2.
(c) Find a matrix A for which col A = nullA.

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