LetΒ \(\rm M=\begin{bmatrix}4&-3\\\ 1&0\end{bmatrix}\)

Consider the following statements:

𝑃: 𝑀8 + 𝑀12 is diagonalizable.

𝑄: 𝑀7 + 𝑀9 is diagonalizable.

Which of the following statements is correct?

1
𝑃 is TRUE and 𝑄 is FALSE
2
𝑃 is FALSE and 𝑄 is TRUE
3
Both 𝑃 and 𝑄 are FALSE
4
Both 𝑃 and 𝑄 are TRUE

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