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Hi. I am wondering if I can get some help on one or two questions on the sheet attached. I have worked out A^2B but am a bit puzzled on the meaning of A^TB. It is probably something very simple but I am struggling could someone help me possibly by listing out steps?.

Also I have worked out A^-1 but am stuck on solving the system of equations. As I though that you have to work out the inverse of a matrix when doing it for equations (AX=B format). although when I work out A ((2,-1)(3,2)(5,3) it is a 3x2 matrix therefore I am unable to get an inverse. Although the numbers are the same as the A^-1 question but just missing 0's therefore I think it may be something to do with that. Could someone help me please.

Thanks

Prab