It is known that square matrix A of order n satisfies A2 + 2a-3e = 0. It is proved that a is invertible and the expression of inverse distance matrix of a is given

It is known that square matrix A of order n satisfies A2 + 2a-3e = 0. It is proved that a is invertible and the expression of inverse distance matrix of a is given


The practice is as follows:
A^2 + 2A =3 E
Factorization a * (a + 2e) / 3 = e
So the inverse matrix of a is (a + 2e) / 3