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2. (i) Let A be an invertible matrix. Assume that A = A-1. What are the possible values for det(A)? (ii) Let B be a skew-symmetric matrix over R, i.e. AT = -B and of order 2n–1. Show that det(B) = 0. (iii) Show that if a square matrix C is hermitian, i.e. C* = C then det(C) is a real number.

2. (i) Let A be an invertible matrix. Assume that A = A-1. What are the possible values for det(A)? (ii) Let B be a skew-symmetric matrix over R, i.e. AT = -B and of order 2n–1. Show that det(B) = 0. (iii) Show that if a square matrix C is hermitian, i.e. C* = C then det(C) is a real number.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. (i) Let A be an invertible matrix. Assume that A = A-1, What are the possible values for det(A)? (ii) Let B be a skew-symmetric matrix over R, i.e. AT = -B and of order 2n-1. Show that det(B) = 0. (iii) Show that if a square matrix C is hermitian, i.e. C* = C then det(C) is a %3D real number.
Transcribed Image Text:2. (i) Let A be an invertible matrix. Assume that A = A-1, What are the possible values for det(A)? (ii) Let B be a skew-symmetric matrix over R, i.e. AT = -B and of order 2n-1. Show that det(B) = 0. (iii) Show that if a square matrix C is hermitian, i.e. C* = C then det(C) is a %3D real number.
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