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Matrices and Determinants question

2014 · Shift 1 · Q35

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PYQ Library
JEE Advanced
Mathematics
Matrices and Determinants
2014 · Shift 1 · Q35

Matrices and Determinants question

2014 · Shift 1 · Q35

JEE AdvancedMathematicsMatrices and DeterminantsMultiple correct+3 / −1

Let M and N be two 3

\times

3 matrices such that MN = NM. Further, if M

e

N2 and M2 = N4, then

A
determinant of (M2 + MN2) is 0
B
there is a 3 $\times$ 3 non-zero matrix U such that (M2 + MN2) U is zero matrix
C
determinant of (M2 + MN2) $\ge$ 1
D
for a 3 $\times$ 3 matrix U, if (M2 + MN2) U equals the zero matrix, then U is the zero matrix

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