Let us consider a 3×3 matrix A with Eigen values of ?1, ?2, ?3 and the Eigen values of A-1 are?
A)?1, ?2, ?3
B)1/?1,1/?2,1/?3
C)-?1, -?2, -?3
D)?1, 0, 0

Question

Quizplus · Accepted Answer

The eigenvalues of the inverse of a matrix A (denoted as A^-1) are the reciprocals of the eigenvalues of A. Therefore, if A has eigenvalues λ1, λ2, λ3, then A^-1 will have eigenvalues 1/λ1, 1/λ2, 1/λ3.

Let Us Consider a 3×3 Matrix a with Eigen Values