M-matrix Inverse Positivity Check

Problem

Return True if the 2x2 matrix A is invertible and every entry of its inverse is non-negative (at least -1e-9).

Such matrices are M-matrices, and their inverses are entrywise non-negative under the usual sign conditions.

Hint

M-matrices have positive diagonal, non-positive off-diagonal, and non-negative inverses.

case 1

in: [[[2,-1],[-1,2]]]

expected: true

case 2

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

expected: false

case 3

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

expected: true

case 4

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

expected: false

Starter codePython

def is_inverse_nonnegative_2x2(A):
    # Your code here
    pass

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