7. Given two ciphers, plaintext may be enciphered by using one of the ciphers, and by then using the other cipher. This procedure produces a product cipher.
a) Find the product cipher obtained by using the transformation $C \equiv 5 P+13$ $(\bmod 26)$ followed by the transformation $C \equiv 17 P+3(\bmod 26)$.
b) Find the product cipher obtained by using the transformation $C \equiv a P+b$ (mod 26) followed by the transformation $C \equiv c P+d(\bmod 26)$, where $(a, 26)=(c, 26)=1$.
7. a) $C \equiv 7 P+16(\bmod 26)$
b) $C \equiv a c P+b c+d(\bmod 26)$