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I need to find a way to quickly calculate the number of the reduced echelon form of a matrix. Is there any?

Example:

$A = $$ \begin{pmatrix} 1 & -1 & 3 & 8 \\ -4 & 2 & 1 & -8\\ -2 & 3 & 5 & 7 \\ \end{pmatrix} $

Let B be the reduced echelon form of

What is the value of $B_{24}$?

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