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While proving that

if A is invertible then, A is row equivalent to I

Steps done are :

  • R be row reduced echelon matrix of A
  • Then R=P*A, where P is finite product of elementary matrices
  • But elementary matrices are invertible, which implies P is invertible
  • Given A is invertible, then R(=P*A) is Invertible
  • Then R is Identity matrix

I understood first four steps.Is there proof, if R is row reduced echelon matrix and is invertible then R is identity ? (Don't use determinants, rank)

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If R is an echelon and invertible matrix then R must be Identity matrix(Must be full rank, because it is invertible).

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