Howdy David, welcome back to the Monastery!

I'm a little surprised that you're getting a value of 3 by evaluating @myMatrix in a scalar context; it should be 2, since @myMatrix is a list with two elements (which just so happen to be array references).

You can get the number of rows and columns in your matrix like this:

$rows = @myMatrix;
$cols = @{ $myMatrix[0] };
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That said, I'd suggest using an existing module for working with matrices instead of rolling your own, unless there's a compelling reason not to. A quick CPAN search finds e.g. Math::GSL::Matrix and Math::Matrix.