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I know this may be a simple question but, aside from row and column operations (with which I have had no luck), is there a clear way to convert a 2x2 matrix Diag(a,b) to the form Diag(1,#)?

Thanks much, Eva

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    Oh, by the way, all the elements belong to the natural numbers so if the upper-left corner is to be one, whatever is there has to be one already because one is the only unit in the natural numbers. I am somewhat confused about this.2011-05-03

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Given that $ \gcd(a,b) = 1, $ and so there are integers $p,q$ such that $ a p + b q = 1, $ your final task is given by the identity $ $

$ \left( \begin{array}{cc} p & q \\ -b & a \end{array} \right) \; \cdot \; \left( \begin{array}{cc} a & 0 \\ 0 & b \end{array} \right) \; \cdot \; \left( \begin{array}{cc} 1 & - b q \\ 1 & 1 - b q \end{array} \right) = \; \;\; \; \left( \begin{array}{cc} 1 & 0 \\ 0 & a b \end{array} \right) $

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    Hi there, Gerry.2011-05-03