CMI-2022-DataScience-A: 6

Question

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.

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