Perspective tool - preserve aspect ratio?

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I was using the Perspective tool (GIMP 2.6) on some photos to correct for some minor rotation/skew issues, and realized how easy it is to throw the image's aspect ratio out of proportion -- in my case, TOO easy.  My photos were of some quilt squares, and I was using the edges of these squares as guides for aligning a Corrective transform to correct for some minor (but visible) skewing.  Naturally, this means I'm aligning my Corrective guide to an area in different proportion to the source image, so it throws the aspect ratio out of whack, and I must have the squares in the photo remain square after transformation....

Is it possible for the tool to compensate for X/Y aspect ratio distortion somehow?  Or is that too much to ask?

On a semi-related note, how does the Perspective transform matrix work?  I get that the first two rows represent an affine transformation, with (1,3) and (2,3) corresponding to X and Y translation, (1,1) and (2,2) corresponding to X and Y scaling.  What's the third row represent?

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Numbers may not lie, but neither do they tell the whole truth.
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