Consider the following relation $R$ on the set of real square matrices of order $3$. $R = \{(A,B) | A = P^{-1}BP \text{ for some invertible matrix } P\}$.
\textbf{Statement-$1$:} $R$ is an equivalence relation.
\textbf{Statement-$2$:} For any two invertible $3 \times 3$ matrices $M$ and $N$,$(MN)^{-1} = N^{-1}M^{-1}$.
\textbf{Statement-$1$:} $R$ is an equivalence relation.
\textbf{Statement-$2$:} For any two invertible $3 \times 3$ matrices $M$ and $N$,$(MN)^{-1} = N^{-1}M^{-1}$.
- AStatement-$1$ is true,Statement-$2$ is true; Statement-$2$ is not a correct explanation for Statement-$1$.
- BStatement-$1$ is false,Statement-$2$ is true.
- CStatement-$1$ is true,Statement-$2$ is true; Statement-$2$ is a correct explanation for Statement-$1$.
- DStatement-$1$ is true,Statement-$2$ is false.
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DifficultJEE MAIN 2021
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