Matrix proof.

**vecoma** · February 25th 2011, 10:33 PM

Hi, i do not know how to go about solving this question. Could someone show me the possible steps to prove this theory? I know what the elementary row operations are... but i still don't know how to prove this. Any help is appreciated. Thank you.

question: If A, B are (n x n) and invertible prove that A can be reduced to B using elementary row operations (elementary matrices).
hint: invertible matrices can be reduced to I

**FernandoRevilla** · February 26th 2011, 02:36 AM

If $R_1,\ldots,R_p$ is a sequence of elementary row operations transforming $A\sim\ldots\sim I$ and $T_1,\ldots,T_q$ is a sequence of elementary row operations transforming $B\sim\ldots\sim I$ then,

$R_1,\ldots,R_p,T_q^{-1},\ldots ,T_1^{-1}$

is a sequence of elementary row operations that transforms $A\sim\ldots\sim B$ .

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