The S$-$bix used in AES is shown as follows:

Given the plaintext $\{0$F$0$E$0$D$0$C$0$B$0$A$09080706050403020100\}$ and the key

$\{02020202020202020202020202020202\}$:

a$.$ Show the original contents of State, displayed as a $44$ matrix.

b$.$ Show the value of State after initial AddRoundKey.

c$.$ Show the value of State after SubBytes.

d$.$ Show the value of State after ShiftRows.