FoundationMultiple choice

For invertible square matrices AA and BB, which identity is correct?

  1. A(AB)−1=A−1B−1(AB)^{-1} = A^{-1}B^{-1}, keeping the original order of the factors
  2. B(AB)⊤=B⊤A⊤(AB)^{\top} = B^{\top}A^{\top}
  3. C(A+B)−1=A−1+B−1(A + B)^{-1} = A^{-1} + B^{-1}
  4. Ddet⁡(A+B)=det⁡A+det⁡B\det(A + B) = \det A + \det B

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For invertible square matrices A and B, which identity is correct? · QuantMax