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Matrices - row equivalent

A is a square matrix. Prove that if A is row equivalent to some square invertible matrix B then A is also invertible.

Help please! :frown:
Original post by Lunu
A is a square matrix. Prove that if A is row equivalent to some square invertible matrix B then A is also invertible.

Help please! :frown:


Well, there's a theorem that says that if A is row equivalent to B, then A=E1E2⋯EnBA=E_1E_2 \cdots E_nB for some elementary matrices EiE_i where an elementary matrix implements an elementary row operation.

Does that help?
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Lunu
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Original post by atsruser
Well, there's a theorem that says that if A is row equivalent to B, then A=E1E2⋯EnBA=E_1E_2 \cdots E_nB for some elementary matrices EiE_i where an elementary matrix implements an elementary row operation.

Does that help?


Yes thank you :smile:

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