It is proved that (1) B + e is an invertible matrix (2) (B + e) ^ (- 1) = 1 / 2 (a + b)` The second question is (B + e) ^ (- 1) = 1 / 2 (a + e)

It is proved that (1) B + e is an invertible matrix (2) (B + e) ^ (- 1) = 1 / 2 (a + b)` The second question is (B + e) ^ (- 1) = 1 / 2 (a + e)

Certificate:
∵AB+A+B=E
∴AB+A+B+E=2E
A(B+E)+(B+E)=2E
(A+E)(B+E)=2E
[(A+E)/2](B+E)=E
According to the definition of the inverse matrix, we can see that:
(B+E)^(-1)=(A+E)/2
That's it!
(a + e) / 2 at the end, did you copy the wrong question