json { "title": "GATE Chemical Engineering 2013 | Matrix Properties: Eigenvalues, Determinant, Rank", "description": "Master linear algebra for GATE Chemical Engineering 2013 with this question on matrix properties. Covers eigenvalues of symmetric matrices, determinant of orthogonal matrices, eigenvalues of transpose, and matrix invertibility based on rank. Practice essential concepts for your exam preparation.", "keywords": "chemical-engineering-gate-2013-question-3, GATE Chemical Engineering, GATE 2013, matrix properties, eigenvalues, symmetric matrix, orthogonal matrix, determinant, transpose, inverse matrix, rank, linear algebra, engineering mathematics, exam preparation, GATE solutions" }

Chemical Engineering > GATE 2013 > Linear Algebra

Which of the following statements are TRUE?
P. The eigenvalues of a symmetric matrix are real
Q. The value of the determinant of an orthogonal matrix can only be +1
R. The transpose of a square matrix A has the same eigenvalues as those of A
S. The inverse of an 'n×n' matrix exists if and only if the rank is less than 'n'

A

P and Q only

B

P and R only

C

Q and R only

D

P and S only

Correct : b

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