Ms Reed's voice slurred her words, And she said things like,'Let A be an n × n matrix with entries R. Define a lineear transformation L: Rn → Rn by L(x) = Ax, For all x in Rn. Whats the answer?' And writes '(a) Show that L is an invertible function if and only if det(A) = 0' and '(b) Show that if L is either one-to-one or onto, then it is invertible.' And Ms. Reed sighs.