a)

The following these steps to construct a Playfair matrix using the key "algorithm":

1. Remove any duplicate letters from the key to avoid redundancy. The resulting key becomes "ALGORITHM."
2. Assign numbers to the remaining unique letters based on their alphabetical order, starting from 0. In this case, we have: A = 0, L = 1, G = 2, O = 3, R = 4, I = 5, T = 6, H = 7, M = 8
3. Create a 5x5 matrix and fill it with the assigned letters from the key, moving from left to right and top to bottom: A L G O R I T H M B C D E F J K N P Q S U V W X Y

This matrix serves as the Playfair matrix, which will be used in Playfair cipher encryption and decryption.

b)

The following these steps to construct a Playfair matrix using the key "cryptography," and assuming  treat redundant letters by removing them after the first occurrence:

1. Remove any duplicate letters from the key after their first occurrence. The resulting key becomes "CRYPTOGAHB."
2. Assign numbers to the remaining unique letters based on their alphabetical order, starting from 0. In this case, we have: C = 0, R = 1, Y = 2, P = 3, T = 4, O = 5, G = 6, A = 7, H = 8, B = 9
3. Create a 5x5 matrix and fill it with the assigned letters from the key, moving from left to right and top to bottom: C R Y P T O G A H B D E F I J K L M N Q S U V W X

This matrix serves as the Playfair matrix for the key "cryptography," with redundant letters removed after their first occurrence.