# GATE Papers >> EEE >> 2019 >> Question No 12

Question No. 12

M is a 2 $\times$ 2 matrix with eigenvalues 4 and 9. The eigenvalues of M2 are

##### Answer : (D) 16 and 81

Solution of Question No 12 of GATE 2019 EEE Paper

Given,

M is a 2 $\times$ 2 matrix with eigen values 4 and 9

$\therefore$     i.e., $\mathrm\lambda=4.9$ [Where $'\mathrm\lambda'$ represents eigen values of M]

From the properties of eigen values; we have if $\mathrm\lambda$ is an eigen value of the matrix M then $\mathrm\lambda^2$ is an eigen value of the matrix M2.

$\therefore\mathrm\lambda^2=4^2,9^2=16.81$ are eigen values of matrix M2.