linear algebra

Question

Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = −1. Then the eigenvalues of the matrix A19 are
(a) 1024 and−1024 (b) 1024√2 and −1024√2
(c) 4√2 and−4√2 (d) 512√2 and−512√2

Answer 1

Option d is right.

Answer 2

eigen values of matrix 1 1

                                       1 -1

are √2 and -√2

now characterstic equation of A^19 is λ^19 ....put λ=+√2 and - √2 you will get (d) as the answer

Comments

but according to the given prb the matrix is like 1       1

                                                                     1      -1

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i have corrected that

please see

Answer 3

Answer is D)