I've spent the past couple hours trying to figure out why this matrix multiplication isn't coming out the way it should.

The problem statement and my work is attached. Basically, I need to verify the theorem that says:

[UT]=[T]*[U]

However, when I multiply [T]*[U], a minus sign gets switched around (see pic).

Also, the bases I'm supposed to use are written on my work (they are different from those in the problem statement).

If anyone could find out what's wrong I'd appreciate it (my brain will too). I'll click the thank you button for you too