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21-07-2017
Mathematics

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let A and B be nxn matrices such that AB is singular prove that either A or Bis singular

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LammettHash LammettHash

21-07-2017

[tex]\det(\mathbf{AB})=\det\mathbf A\times\det\mathbf B[/tex]

Because [tex]\mathbf{AB}[/tex] is singular, we have

[tex]\det(\mathbf{AB})=0[/tex]

from which it follows that either [tex]\det\mathbf A=0[/tex] or [tex]\det\mathbf B=0[/tex].

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