Null matrix and invertible matrix

[seema283k]

how can we use property of null matrix .explain it by giving examples.
please give me explanation of the theorem----if A is a null matrix & B is any matrix then I+AB is invertible iff I+BA is invertible

 

[ygolo]

Are you sure you mean the null matrix?

Because the null matrix is the matrix with all zero entries.

So if A is the null matrix, then I+AB=I=I+BA. I is invertible. So for your theorem, both the hypothesis and conclusion are true (in both directions). Making the theorem vacuously true.