Prove or disprove each of the following statements. (c) If C is a real square matrix, then C2 + I (I is the identity matrix ) isnon-singular.(d) The vector spaces U = {M € R³×3 : M = MT} and V = {N E R3x3 :the sum of the entries in each row of N is equal to 0} are isomorphic.

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(c) If C is a real square matrix, then C2 + I (I is the identity matrix) is non-singular.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Determinants

Section3.3: Properties Of Determinants

Problem 63E: Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.

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Question

Prove or disprove each of the following statements.

(c) If C is a real square matrix, then C2 + I (I is the identity matrix ) is
non-singular.
(d) The vector spaces U = {M € R³×3 : M = MT} and V = {N E R3x3 :
the sum of the entries in each row of N is equal to 0} are isomorphic.

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