Let \(M = \begin{bmatrix} 4 & -3 \\ 1 & 0 \end{bmatrix}\). Consider the following statements:
\(P:\ M^8 + M^{12}\) is diagonalizable.
\(Q:\ M^7 + M^9\) is diagonalizable.
Which of the following statements is correct?
(A) $𝑃$ is $TRUE$ and $𝑄$ is $FALSE$
(B) $𝑃$ is $FALSE$ and $𝑄$ is $TRUE$
(C) Both $𝑃$ and $𝑄$ are $FALSE$
(D) Both $𝑃$ and $𝑄$ are $TRUE$
