GATE Electrical 2019 | Question: 2

Question

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

• A. $4$ and $9$
• B. $2$ and $3$
• C. $-2$ and $-3$
• D. $16$ and $81$

Answer 1

Answer D:

By using properties of eigen values of a matrix:

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