
Matrix proof.
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

If $\displaystyle R_1,\ldots,R_p$ is a sequence of elementary row operations transforming $\displaystyle A\sim\ldots\sim I$ and $\displaystyle T_1,\ldots,T_q$ is a sequence of elementary row operations transforming $\displaystyle B\sim\ldots\sim I$ then,
$\displaystyle R_1,\ldots,R_p,T_q^{1},\ldots ,T_1^{1}$
is a sequence of elementary row operations that transforms $\displaystyle A\sim\ldots\sim B$ .