Find a 4 4 matrix with entries 1 or 1 whose determinant is

Find a 4 × 4 matrix with entries 1 or -1 whose determinant is 16 (Hint: Consider finding first an orthonormal basis of R⁴ whose vectors’ entries are 1/2 or 1/2 ).

Solution

The matrix given below has determinant 16 -1.000 -1.000 -1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 1.000 -1.000 -1.000 -1.000 1.000 1.000 -1.000