Gradient of Determinant

Problem

Return the gradient of det(A) with respect to the 2x2 matrix A.

For A = [[a, b], [c, d]] the gradient is the cofactor matrix [[d, -c], [-b, a]].

Hint

The derivative of det(A) is the adjugate transpose, which for 2x2 is the cofactor matrix.

case 1

in: [[[1,2],[3,4]]]

expected: [[4,-3],[-2,1]]

case 2

in: [[[2,0],[0,3]]]

expected: [[3,0],[0,2]]

case 3

in: [[[1,0],[0,1]]]

expected: [[1,0],[0,1]]

case 4

in: [[[1,2],[2,4]]]

expected: [[4,-2],[-2,1]]

Starter codePython

def grad_det_2x2(A):
    # Your code here
    pass

4 test cases · run your code against them in the editor