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2D Transformation Query

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I think I've answered my own question here:

I'm basically wanting the vector (0,0) to translate to (0,0).

So if I translate (0,0) by the orginal matrix, I'll get some vector (x,y). Now if I do a translation operation on my matrix with the vector (-x,-y), It'll translate itself back to the origin (and (0,0) will transform to (0,0)).

Yes?

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[ a b c ] * [ x ]
[ d e f ] [ y ]
[ 0 0 1 ] [ 1 ]
= [ x * a + y * b + c d * x + e * y + f 1 ]


Just set c and f to 0.

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