A number theory problem by Rocco Dalto

Number Theory Level pending

Using a hill cipher, find the $$5 \times 5$$ matrix $$A$$ modulo 26 that replaces the plaintext word $$immunoelectrophoretically$$ with the ciphertext word $$phosphatidylethanolamines$$, where $$a \rightarrow 0, b \rightarrow 1, \ldots , z \rightarrow 25$$. 

Express the answer as the $$\det(A)$$ modulo 26.

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