Question

Let $T$ & $U$ be the set of all orthogonal matrices of order $3$ over $R $ & the set of all non-singular matrices of order$ 3$ over $R$ respectively
Let $A=\{-1,0,1\}$, then

• A. there exists bijective mapping between $A$ and $T, U$.
• B. there does not exist bijective mapping between $A$ and $T, U$.
• C. there exists bijective mapping between $A$ and $T$ but not between $A\, \&\, U$.
• D. there exists bijective mapping between $A$ and $U$ but not between $A\, \&\, T$.

Answer 1

Answer: (B)

As $n(A) \neq n(T)$ and $n(A) \neq n(u)$