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n x n matrix A is called skew-symmetric if AT = -A. Show that is A is skew sy

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 63EQ

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Question

An n x n matrix A is called skew-symmetric if A^T = -A. Show that is A is skew symmetric and n is an odd integer, then A in not invertible. (Hint: Use determinants.)

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