(i) Let R := cos(0) - sin (0) cos(ke ) - sin(ke ) sin(0) cos(0) For all nonnegative integers k, show that Rk = sin(ke) cos(ke (ii) In 1969, Volker Strassen surprised the mathematical community by showing that two (2 x 2)-matrix can be multiplied using only seven multiplications of scalars. Establish his method by showing that, when A := a c b d] P1 := (atd) (w+z) p3 : a(y -z) ps := (a+ c)z P7 := (c- d) (x+z), B := W y x Z P2 := ( b + d) w p4 : d(x - w) p6 := (b -a) (wty) we have A B = P1 + P4 - P5 + P7 P3 + P5 P2 + P4 P1 +P3 - P2+ P6