Question

If 3, 5 are the eigenvalues of a square matrix A of order 2, then the eigenvalues of the matix A³ will be
1. 27, 125
2. 9, 15
3. 3, 5
4. 9, 25

Answer 1

Correct Answer - Option 1 : 27, 125

Concept:

If λ is an eigenvalue of a matrix A and k  is a scalar then:

1) λ^m is the eigenvalue of matrix A^m (m belongs to N).

2) kλ  is an eigenvalue of matrix kA.

3) λ + k is an eigenvalue of the matrix A + kI.

4) λ - k  is an eigenvalue of matrix A - kI.

Calculation:

Given:

3, 5 are the eigenvalues then,

Using Property 1;

A³ = λ³ = 3³ = 27.

A³ = λ³ = 5³ = 125.