Determine if the statement is true or false and

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Determine if the statement is true or false, and justify your answer. You may assume thatAandBarematrices.Ifthen eitherorn×nAB.True. Ifij, thenAij=Bij= 0, so (AB)ij= 0, andABis diagonal.True. Ifi=j, thenAij=Bij= 0, so (AB)ij= 0, andABis diagonal.False. Ifi=j, then (AB)ij=AijBijmay not be zero, soABis not necessarily diagonal.False. Ifij, then (AB)ij=AijBijmay not be zero, soABis not necessarily diagonal.False. Ifij, thenAij= −Bij, so (AB)ij= 2Aij, andABis not diagonal.n×nAB=BA,A=InB=In.True.AB=BAcan only be true if eitherA=InorB=In.False. For example,A=B= 0nn.False. For example,A=,B=.0110−1001False.AB=BAfor any matricesAB.False. For example,A=,B=.01101001
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Term
Fall
Professor
N/A
Tags
Math, Matrices,

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