$(12\backslash \%)$ Consider a Hill cipher that uses a $\backslash (2\backslash$times $2\backslash )$ square matrix $\backslash ($ A $\backslash )$ as key. The elements of $\backslash ($ A $\backslash )$ are integers in $\backslash ($ Z$\_\{26\}\backslash )$ that encodes the $26$ English alphabets as follows:

Suppose the application of this Hill cipher yields the following results:

$-$ The plaintext $"$ba$"$ is encrypted into ciphertext $"$FD$".$

$-$ The plaintext $"$zz$"$ is encrypted into ciphertext $"$JQ$".$

Based on the above known plaintext results, please derive the key $\backslash ($ A $\backslash )$ of the given Hill cipher.