The trace of a square matrix A, denoted by tr(A), is defined as the sum of the main diagonal e of A. If X and Y are n-by-n matrices, which of the following is a true statement? (b) If tr(X) = 0, then X = On- (d) tr(XY) = tr(YX). (a) tr(X²) = [tr(X)]². (c) tr(XY) = tr(X)tr(Y).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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The trace of a square matrix A, denoted by tr(A), is defined as the sum of the main diagonal entries
of A. If X and Y are n-by-n matrices, which of the following is a true statement?
(a) tr(X²) = [tr(X)]².
(c) tr(XY) = tr(X)tr(Y).
(b) If tr(X) = 0, then X = On.
(d) tr(XY) = tr(YX).
Transcribed Image Text:The trace of a square matrix A, denoted by tr(A), is defined as the sum of the main diagonal entries of A. If X and Y are n-by-n matrices, which of the following is a true statement? (a) tr(X²) = [tr(X)]². (c) tr(XY) = tr(X)tr(Y). (b) If tr(X) = 0, then X = On. (d) tr(XY) = tr(YX).
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