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

$.$ X is a

matrix below.

Encryption function:

Here we know neither

nor

but an attack on this cryptosystem told us that the plaintext 'LEMONS' was encrypted as 'KZKOSB'. i$.$e$.$ LEMONS

KZKOSB.

First find

and

$,$ the private key. Input each matrix entry as an integer between $0$ and $25$ ie a member of

$.$

;

$.$

Hence, decrypt 'PWLOZE' in this cryptosystem. PWLOZE

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