Mathematics, Data Science, Algebra, Numerical Analysis, University At Buffalo.
if AB = BA = I. If so, we denote A⁻¹ = B. You can easily show that det(A⁻¹) = (det(A))⁻¹. If det(A) ≠ 0, then det(A⁻¹) is defined, hence A⁻¹ must exist. If det(A) = 0, then det(A⁻¹) is undefined, hence A⁻¹ does not exist. In summary, Matrix is a very important mathematical concept and is crucial