In the JEE paper of yesterday, one of the math question reads " Let M and N be two 3 × 3 non-singular skew symmetric matrices" I had thought that all odd order skewsymmetric matrices are singular. Is the question wrong? Of course, one can solve the question assuming M and N are 4 x 4 matrices and arrive at the answer (-M^2) but my point is the question wrong?
Indeed.
ReplyDeletedet(A) always equals det(A^T).
But since A is skew-symmetric, i.e., A = -A^T, we get
det(-A^T) = det(A^T)
i.e., (-1)^3 det(A^T) = det(A^T).
It follows that A is singular and the problem is self-contradictory.
Are making wrong questions a process of testing? If not how can such high faculty do it ! It sometimes leave me blanked ?
ReplyDelete