I really need a solution, and explanation to that solution. I found this really hard

Question

Raj encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear text code for each letter by the matrix C=  to get a matrix that represents the encoded text. The matrix representing the encoded text is below. 

What is the secret phrase? Determine the location of spaces after you decode the text.

Answer 1

Let

C be the given 2x2 code matrix,

E be the given 2x7 matrix of encoded text,

T be the unknown matrix of plain text.

The statement of the problem has the sentence

"he multiplied the clear text code for each letter by the matrix C".

That implies either T × C = E or C × T = E.

T × C would yield a matrix with 2 columns, while E has seven columns.

Therefore it must be

C × T = E (1)

and T must be a 2×7 matrix.

We can calculate T by multiplying both sides of (1) with the inverse C^-1 of C on the left

C^-1 × C × T = C^-1 × E

T = C^-1 × E

At this point you need to

a) calculate the inverse C^-1

b) perform the the multiplication C^-1 × E

c) replace the resulting numbers in T by their corresponding letters

d) insert blanks to make it valid English.

a), b), and c) are tedious, but you can write a simple computer program to do them for you.

If you cannot do that, then there are web site that will do a) and b) for you.

If you are not allowed any automation, then this is just a very tedious exercise in arithmetic.

Answer 2