PG entrance exam CUET PG 2025 Mock Test Mathematical Science Linear Algebra Eigenvalues and Eigen Vectors
Consider the following statements where X and Y are nxn matrices with real entries then which of the following is(/ are) correct::
(A). If P-1XP is diagonal matrix for some real invertible matrix P, then there exists a basis for Rn consisting of eigenvectors of X.
(B). If X is diagonal matrix with distinct diagonal entries and XY = YX, then Y is also diagonal matrix.
(C). If X2 is diagonal matrix, then X is diagonal matrix.
(D). If X is diagonal matrix and XY = YX for all Y, then \(X=\lambda \mid\) for some \(\lambda \in {R}\)
Choose the correct answer from the options given below
1
(A), (B) and (D) only.
2
(A), (B) and (C) only.
3
(A), (B), (C) and (D).
4
(B), (C) and (D) only.