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 $n(A)\ne n(T)$ and $n(A)\ne n(u)$