This matrix is said to be quickly solvable but im not sure of the trick:

-1 1 1 1 1

1 -1 1 1 1

1 1 -1 1 1

1 1 1 -1 1

1 1 1 1 -1

the matrix is all 1's with -1's on the main diagonal, im not sure if i should row reduce until i have an upper triangular matrix and use product of diagonal entries or if there is a simple trick im missing

Additional Details

the answer is 48 according to my ti-89