Which of the following subsets of the sets in the set of real square matrices of size 2 x 2 is closed for the usual operation of matrix multiplication? (a) {A ∈ R^2x2 | matrix trace A= 0} (b) {A ∈ R^2x2 |  A^2 = 0} (c) {A ∈ R^2x2 | det A= 0} (d) {A ∈ R^2x2 | matrix trace A= 2} (e)  {A ∈ R^2x2 | det A= 2}..

Elementary Linear Algebra (MindTap Course List)
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Chapter3: Determinants
Section3.CM: Cumulative Review
Problem 17CM: Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]
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Which of the following subsets of the sets in the set of real square matrices of size 2 x 2 is closed for the usual operation of matrix multiplication?

(a) {A ∈ R^2x2 | matrix trace A= 0}

(b) {A ∈ R^2x2 |  A^2 = 0}

(c) {A ∈ R^2x2 | det A= 0}

(d) {A ∈ R^2x2 | matrix trace A= 2}

(e)  {A ∈ R^2x2 | det A= 2}..

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