Question

Let $P$ be the set of all non-singular matrices of order $3$ over $R$ and $Q$ be the set of all orthogonal matrices of order $3$ over $R$. Then,

• A. $P$ is proper subset of $Q$
• B. $Q$ is proper subset of $P$
• C. Neither $P$ is proper subset of $Q$ nor $Q$ is proper subset of $P$
• D. $P\cap Q=\varphi ,$ the void set

Answer 1

Answer: (B)

All the orthogonal matrix are non-singular matrix.
$\therefore Q$ is proper subset of $P$.