Which of the following regulations defines the associative binary operation ° on the set R^n×n (n>=2)? Here, A, B ∈ R^n×n are arbitrary matrices. (a) A ° B = AB + BA (b) A ° B = AB - BA (c) A ° B = A + AB + B (d) A ° B = A^t (e) None of the above.

Which of the following regulations defines the associative binary operation ° on the set R^n×n (n>=2)? Here, A, B ∈ R^n×n are arbitrary matrices. (a) A ° B = AB + BA (b) A ° B = AB - BA (c) A ° B = A + AB + B (d) A ° B = A^t (e) None of the above.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.5: Determinants

Problem 82E: Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.

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Question

Which of the following regulations defines the associative binary operation ° on the set R^n×n (n>=2)? Here, A, B ∈ R^n×n are arbitrary matrices.

(a) A ° B = AB + BA

(b) A ° B = AB - BA

(d) A ° B = A^t

(e) None of the above.

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