Let $S =\{A=[a_{ij}]_{n\times n}:a_{ij}\in\{0,1,2,3,4,5\}\}$, B and C are subset of S s.t. $B=\{A\in S:|A|=1\}$ and $C=\{A\in S:|A|=-1\}$. Then for n>=2 which is true..

1)B and C are finite sets.
2)B and C are infinite sets.
3)|B|=|C| if n>=2
4)|B| not equal to |C|

  • $\begingroup$ What are your thoughts on this problem? What have you tried so far? $\endgroup$ – Omnomnomnom Sep 11 at 16:36
  • $\begingroup$ Also, does $|A|$ refer to the determinant of $A$ in this context? $\endgroup$ – Omnomnomnom Sep 11 at 16:37
  • $\begingroup$ Yes..|A|= det A, but since B, C are sets then |B|,|C| refers to number of elements in the sets B and C. $\endgroup$ – Abhinandan Saha Sep 11 at 16:46


  • Any subset of a finite set is finite
  • Switching the first two rows of any matrix with determinant $1$ produces a matrix with determinant $-1$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.