Question
Mathematics Question on Matrices and Determinants
Let 𝑃 be a 3×3 matrix having the eigenvalues 1,1 and 2. Let (1,−1,2) 𝑇 be the only linearly independent eigenvector corresponding to the eigenvalue 1. If the adjoint of the matrix 2𝑃 is denoted by 𝑄, then which of the following statements is/are TRUE?
A
trace(𝑄)=20
B
det(𝑄)=64
C
(2, −2, 4)𝑇 is an eigenvector of the matrix Q
D
𝑄 3=20𝑄 2−124𝑄+256𝐼3
Answer
trace(𝑄)=20
Explanation
Solution
The correct options are: A and C