Null matrix and invertible matrix

  1. 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
  2. jcsd
  3. 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.
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