Mention appropriate theorems from the textbook in your explanations following (i.e. mention when you use certain properties of the determinant deriving these expressions): (a) Show that if A is invertible, then det(A¯¹) = = 1 det(A) (b) Let A and P be square matrices, with P invertible. Show that det(PAP- det(A).

I need some help with a linear algebra problem involving traffic flow networks.  The goal is to find the flow rates (f1 through f5) and analyze an augmented matrix. When I did this, I got confused in finding the flow rates... my answer doesn't resemble the vector format it should look like (shown in the last figure). Could I get some assistance to better understand how to set up this problem and find the flow rates? Thank you.

Please assist in answering this question

This is a Linear Algebra problem. Please explain each step clearly, no cursive writing.