peyto1011 peyto1011

19-07-2019
Mathematics

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Prove that if AB= 0and A is invertible then B= 0

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windyyork windyyork

28-07-2019

Answer with Step-by-step explanation:

Since we have given that

AB = 0 and A is invertible so, AA⁻¹ = I

So, Consider,

[tex]AB=0[/tex]

Multiplying A⁻¹ on both the sides, we get that

[tex]A^{-1}AB=A^{-1}0\\\\(AA^{-1})B=0\\\\IB=0\\\\B=0[/tex]

Hence proved.

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