Assume Fred sees your RSA signaure on m1 and m2, (i.e., he sees (md1 mod n) and (md2 mod n).
Discuss how does he calculate the signature on each of mj1 mod n (for positive integer j), m−1
1 mod n,
m1 × m2 mod n, and in general mj1 × mk2 mod n (for arbitrary j and k)?