cmi-entrance 2016 Q6

cmi-entrance · India · pgmath 4 marks Groups Centre and Commutant Computation
What is the cardinality of the centre of $O_2(\mathbb{R})$? (Definition: The centre of a group $G$ is $\{g \in G \mid gh = hg \text{ for every } h \in G\}$. Hint: Reflection matrices and permutation matrices are orthogonal.)
(A) 1;
(B) 2;
(C) The cardinality of $\mathbb{N}$;
(D) The cardinality of $\mathbb{R}$.
What is the cardinality of the centre of $O_2(\mathbb{R})$? (Definition: The centre of a group $G$ is $\{g \in G \mid gh = hg \text{ for every } h \in G\}$. Hint: Reflection matrices and permutation matrices are orthogonal.)\\
(A) 1;\\
(B) 2;\\
(C) The cardinality of $\mathbb{N}$;\\
(D) The cardinality of $\mathbb{R}$.