-2 and -3
2 and 3
4 and 9
16 and 81
Answer is Right!
Answer is Wrong!
The correct answer is $\boxed{\text{D. }16 \text{ and }81}$.
The eigenvalues of a matrix are the roots of its characteristic polynomial. The characteristic polynomial of a 2×2 matrix $M$ is given by:
$$p(x) = |xI – M|$$
where $I$ is the identity matrix.
If the eigenvalues of $M$ are $\lambda_1$ and $\lambda_2$, then the eigenvalues of $M^2$ are $\lambda_1^2$ and $\lambda_2^2$.
In this case, the eigenvalues of $M$ are $4$ and $9$, so the eigenvalues of $M^2$ are $4^2 = 16$ and $9^2 = 81$.