GATE Overflow | Mathematics | Test 1 | Question: 3

Question

$A$ is a $2\times 2$ matrix with eigenvalues $2$ and $-3$. The eigenvalues of the matrix $A^2$ are?

• A. 4,-9          
• B. 2,-3        
• C. 4,9        
• D. can not be determined from given data

Answer 1

If x₁, x_2, x₃,.....x_n be the eigen values of a matrix A. Then the eigen values of Aⁿ are x₁ⁿ, x₂ⁿ , x₃ⁿ .....x_nⁿ  So here the eigen values of A are 2 and -3. So eigen values of A² will be (2)² = 4  and (-3)² = 9 .

Answer 2

ans is 4,9
as applying |x|^2