Question 50

Mathematics Matrices Medium

Let us consider a square matrix \( A \) of order \( n \) with eigenvalues \( a, b, c \). Then the eigenvalues of the matrix \( A^\top \) could be:

(A) (a,b,c)
(B) \( (-a,-b,-c) \)
(C) \( (a-b, b-a, c-a) \)
(D) \( (a^{-1}, b^{-1}, c^{-1}) \)
View Dynamic Solution & Explanation
Correct Solution: Option A

Step-by-step Solution:

The eigenvalues of a square matrix ( A ) and its transpose \( A^\top \) are identical. That is, if ( a, b, c ) are eigenvalues of ( A ), then the same values are the eigenvalues of \( A^\top \). This property holds because eigenvalues are invariant under transposition.
Correct Option: (a)