A = [1 3 1 1 1 -1 3 11 6] iA = inv(A) A * iA det(A * iA) L, U = lu(A, Val{false}) L U L * U [1 2 3; 4 5 6]' Q = [1/3 2/3 2/3; 2/3 1/3 -2/3; 2/3 -2/3 1/3] isapprox(inv(Q), Q') B = [4 -2 -7 -4 -8 9 -6 -6 -1 -5 -2 -9 3 -5 2 9 7 -9 5 -8 -1 6 -3 9 6] L, U, p = lu(B) L U p