Consider the following assertions i. rank (st) = rank s = rank t jk rank (st) = rank s, if t is non-singular ill. rank (st) = rank t, if t is non-singular where

Consider the following assertions I. Rank (ST) = Rank S = Rank T JK Rank (ST) = Rank S, if T is non-singular Ill. Rank (ST) = Rank T, if T is non-singular where S,T :V> V are linear transformations of a finite dimensional vector space V. Which of these is/are correct? (a) only (c) I and Il b only II (d) Il and lll