Alyssa H.

asked • 09/24/20

Select all statements below which are true for all invertible 𝑛×𝑛 matrices 𝐴 and 𝐵

  1. ABA-1=B
  2. (A+A-1)9=A9+A-9
  3. A+B is invertible
  4. (In-A)(In+A)=In-A2
  5. (A+B)2=A2+B2+2AB
  6. A5 is invertible

1 Expert Answer

By:

Greg K.

#4 is not true, A+B is not always invertible. Take for example the 2x2 invertible matrices (1, 0)(0, 4) and (1,0)(0, -4) (format is (row1)(row2)). The addition of these matrices makes (2,0)(0,0), a matrix that is not invertible.
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12/15/21

Greg K.

I meant #3****, sorry.
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12/15/21

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