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Answer as T or F:

1) Every linear system consisting of 3 equations in 4 unknowns has infintely many solutions.

2) If A and B are 3 x 3 matrices , then det(AB - A (B^T) ) = 0

3) If A and B are n x n matrices, nonsingular matrices and AB=BA, then A(B^-1) = (B^-1)A

4) If A is a singular n x n matrix, then Aadj(A)=0

For (1):

I think its true

since # of columns > # of rows

so we will have recall a parameter

and this means we will a infinitely many solutions

For (2):

I do not know how to do it =(

For (3):

I got the answer, its true

but how ?

For (4):

I completely stopped here :/

Any help please?

this is not for my homework

I swear

am solving these for fun