$M$  is $2 \times 2$ matrix with eigenvalues $4$ and $9.$ The eigenvalues of $M^{2}$ are

1. $4$ and $9$
2. $2$ and $3$
3. $-2$ and $-3$
4. $16$ and $81$
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The eigenvalues of M$^{2}$ are 4$^{2^{^{}}}$ and 9$^{^{2}}$, i.e, 16 and 81 respectively