I find it amusing that you'd ask for "some Proof" that your car is not a hybrid. Open the hood; do you see a big aluminum-covered inverter box that says "Hybrid" on it? No, of course you don't. Any "Hybrid" badges on the exterior? No, of course not. Does the engine shut-off when you're stopped at traffic lights, and re-start automatically when you step on the gas? No, of course it doesn't.
The Matrix in 2007 wasn't available as a hybrid, nor 2008, 2009, and the current model year (2010) isn't available as a hybrid either. Maybe in some future model year.
The only hybrids that Toyota sells are the Prius (available only as a hybrid), the Camry, and the Highlander.
Edit: Another answer that you've received references the lack of a "hybrid synergy drive" badge. That's not accurate, as Toyota didn't start using that term until the 2004 Prius. Earlier models just had a "hybrid" badge.
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Is my Toyota Matrix 2007 a Hybrid?
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