SOLUTION: Find det A, given A = [-1 0 1 2-1 3 0 1 5]

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This one is not easy to show here, but we can do it by the reduction-by-minors technique:
(-1) times the rows and columns not including the -1 MINUS
(0) times the rows and columns not including the 0 PLUS
(1) times the rows and columns not including the 1
so we get
(-1)(-5 - 3) - 0 + 1(2 - 0) =
8 - 0 + 2 =
10