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CMI-2022-DataScience-A: 6

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A matrix $C$ is said to be symmetric if $C^{T}=C$. Which of the following is/are true? Let $A, B$ be $n \times n$ matrices.

  1. If $A$ is symmetric and invertible, then $A^{-1}$ is also symmetric and invertible.
  2. If $A$ and $B$ are symmetric, then $C=A B$ is also symmetric.
  3. If $A$ and $B$ are invertible, then $C=A B$ is also invertible.
  4. If $A$ and $B$ are symmetric, then $D=A+B$ is also symmetric.
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