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CMI-2022-DataScience-A: 5

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Let $A, B$ be $n \times n$ invertible matrices of real numbers. Let $C=I+A A^{T}, D=I+B A A^{T} B^{T}$. We can conclude that

  1. $(A B)^{-1}=\left(I+B^{-1} A^{-1}\right)$
  2. $(A B)^{-1}=A^{-1} B^{-1}$
  3. $C=C^{T}$
  4. $D=D^{T}$
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