An m × n matrix A is said to have a right inverse if there exists an n x m matrix C such that AC = Im. A is said to have a left inverse if there exists an n × m matrix D such that DA = In.
(a) If A has a right inverse, show that the column vectors of A span Rm.
(b) Is it possible for an m × n matrix to have a right inverse if n < m? n ≥ m? Explain.