Show that if Y (t); an n by n matrix, is the unique maximal solution of the

matrix IVP

Y'(t) = A*Y(t); Y (0) = I;

then Y has the characteristic property of exponentials, namely

Y (s + t) = Y (s)Y (t) for all s; t E(element of) R.

and

Y (-t) = Y(t)^-1