1
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

Let $$\omega$$ be a complex cube root of unity with $$\omega$$ $$\ne$$ 1 and P = [pij] be a n $$\times$$ n matrix with pij = $$\omega$$i + j. Then P2 $$\ne$$ 0, when n = ?

A
57
B
55
C
58
D
56
2
JEE Advanced 2013 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-0
For 3 × 3 matrices M and N, which of the following statement(s) is(are) NOT correct?
A
NTMN is symmetric or skew symmetric, according as M is symmetric or skew symmetric.
B
MN – NM is skew symmetric for all symmetric matrices M and N.
C
MN is symmetric for all symmetric matrices M and N.
D
(adj M)·(adj N) = adj(MN) for all invertible matrices M and N.
3
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-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)

A
$$-$$2
B
$$-$$1
C
1
D
2
4
IIT-JEE 2011 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1

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

A
M2
B
$$-$$N2
C
$$-$$M2
D
MN
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