The AES encryption consists of applying the following transformations: AddRoundKey $->$ SubBytes $->$ ShiftRows $->$ MixColumns $->$ AddRoundKey $->$ SubBytes $->,$ while the decryption process applies the transformations: AddRoundKey $->$ ShiftRows$1->$ SubBytes$1->$ AddRoundKey $->$ MixColumns$1->$ ShiftRows$1->$

a$)$ Explain why the order of ShiftRows$1$ and SubBytes$1$ can be interchanged.

b$)$ Both MixColumns and its inverse MixColumns$1$ are linear transformations on the block of bytes. Explain how you can interchange the order of MixColumns$1$ and AddRoundKey in the encryption process. $($A modification in the round key is needed$).$

c$)$ Using the previous points, show that the decryption of AES can be done in the following way: AddRoundKey $->$ SubBytes$1->$ ShiftRows$1->$ MixColumns$1->$ AddRoundKey $->$ Note that the order of the steps corresponds to the order in the encryption process.