37 let m, ir) denote the space of all nx n atrices f with entries from a field r. let matrix a =ae m, (r) be a non-zero nilpotent matrix and consider the linear

37 Let M, IR) denote the space of all nx n atrices f with entries from a field R. Let matrix A =ae M, (R) be a non-zero nilpotent matrix and consider the linear map T: M, (R)> M, (R) given by T(X) = BX, map where B= A-I. Then choose the correct? (a) Trace (T) =-n (b) Rank (T) = n (c) Tis non-singular (d) None of these