A = {{1, 1}, {1 + 10^-5, 1}}

Det[A]

J = Inverse[A]

N[Eigenvalues[A . Transpose[A]]]

N[Eigenvalues[J . Transpose[J]]]

b = {2, 2 + 10^(-5)}

x = J . b

b1 = {2, 2}

x1 = J . b1