Does the security of the Hill cipher machine, utilizing a $2-$by$-2$ matrix as its key, remain resilient against the following types of attacks?

$($a$)$ Ciphertext only attack. $($b$)$ Chosen plaintext attack. $($c$)$ Chosen ciphertext attack.

If no$,$ explain why; if yes, show how you can get the key?

Note: For all the three attacks mentioned above, in both cases $($whether the answer is $$no$$ or $$yes$),$ show a worked$-$out example with appropriate numbers to justify your answer