JEE Advanced 2013 Paper 1 Offline | Matrices and Determinants Question 31 | Mathematics

JEE Advanced 2013 Paper 1 Offline

MCQ (More than One Correct Answer)

-0

For 3 × 3 matrices M and N, which of the following statement(s) is(are) NOT correct?

N^TMN is symmetric or skew symmetric, according as M is symmetric or skew symmetric.

MN – NM is skew symmetric for all symmetric matrices M and N.

MN is symmetric for all symmetric matrices M and N.

(adj M)·(adj N) = adj(MN) for all invertible matrices M and N.

IIT-JEE 2012 Paper 2 Offline

MCQ (More than One Correct Answer)

-1

If the ad joint of a 3 $$\times$$ 3 matrix P is $$\left[ {\matrix{ 1 & 4 & 4 \cr 2 & 1 & 7 \cr 1 & 1 & 3 \cr } } \right]$$, then the possible value(s) of the determinant of P is(are)

$$-$$2

$$-$$1

IIT-JEE 2011 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

Let M and N be two 3 $$\times$$ 3 non-singular skew symmetric matrices such that MN = NM. If P^T denotes the transpose of P, then M²N²(M^TN)^$$-$$1(MN^$$-$$1)^T is equal to

M²

$$-$$N²

$$-$$M²

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