Tricky Matrix Problem with clever solution: Crack the cipher key and decrypt the message below $...$ this is a scaffold problem for Q$3.$

All arithmetic is done in $Z_{26}.x$ is a $21$ matrix below.

Encryption function: $f_E(x)=x+mod26$

Here we know neither $$ nor $$ but an attack on this cryptosystem told us that the plaintext 'DARTED' was encrypted as 'IWHEJR'. i$.$e$.$ DARTED $f_E$ IWHEJR.

First find $$ and $,$ the private key. Input each matrix entry as an integer between $0$ and $25$ ie a member of $Z_{26}.$

Hence, decrypt $\text{'}$PBXRRR$\text{'}$ in this cryptosystem. PBXRRR $f_D$

input a $6-$letter answer: $2+2+2)$

HELLO TO AID THE BOTTOM RIGHT VALUE OF THE ALPHA MATRICES IS ZERO AND THIS IS CORRECT.