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Let M and N be two 3xx3 matrices such th...

Let M and N be two `3xx3` matrices such that `MN=NM`. Further, if `M ne N^(2)` and `M^(2)=N^(4)`, then

A

determinant of `(M^2+MN^2)` is 0

B

there is a 3 x 3 non-zero matrix U such that `(M^2+MN^2)` U is zero matrix

C

determinant of `(M^2+MN^2) ge 1`

D

for a 3 x 3 matrix U, if `(M^2+MN^2)U` equals the zero matrix , then U is the zero matrix

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The correct Answer is:
A, B
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
  1. How many 3xx3 matrices M with entries from {0, 1, 2} are there, for wh...

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  2. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

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  3. Let M and N be two 3xx3 matrices such that MN=NM. Further, if M ne N^(...

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  4. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

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  5. the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha...

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  6. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

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  7. If the adjoint of a 3 xx 3 matrix P is [{:(,1,4,4),(,2,1,7),(,1,1,3):}...

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  8. Let X \ a n d \ Y be two arbitrary, 3xx3 , non-zero, skew-symmetric ma...

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  9. Which of the following values of alpha satisfying the equation |(1+alp...

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  10. Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[...

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  11. Let alpha, lambda , mu in R.Consider the system of linear equations ...

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  12. Which of the following is(are) NOT of the square of a 3xx3 matrix with...

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  13. Let S be the set of all column matrices [(b(1)),(b(2)),(b(3))] such th...

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  14. M=[{:(sin^(4)theta,-1-sin^(2)theta),(1+cos^(2)theta,cos^(4)theta):}]=a...

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  15. Let M=[{:(0,1,a),(1,2,3),(3,b,1):}]and adj M =[{:(-1,,1,,-1),(8,,-6,,2...

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  16. For positive numbers x, y and z, the numerical value of the determinan...

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  17. The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| ...

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  18. If x=-9 is a root of |(x,3,7),(2,x,2),(7,6,x)|=0 then other two roots ...

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  19. Sum of real roots of the euation |{:(1,4,20),(1,-2,5),(1,2x,5x^(2)):}|...

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  20. "Let "plambda^(4) + qlambda^(3) +rlambda^(2) + slambda +t =|{:(lambda^...

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