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Let P and Q be 3xx3 matrices P ne Q. If ...

Let P and Q be `3xx3` matrices `P ne Q`. If `P^(3)=Q^(3)` and `P^(2)Q=Q^(2)P`, then determinant of `(P^(2)+Q^(2))` is equal to :

A

0

B

-1

C

-2

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `P^(3) = Q^(3)" "...(i) `
` and P^(2) Q = Q^(2) P " "...(ii)`
Subtracting Eq. (i) and (ii), we get
`P^(3) - P^(2) Q = Q^(3) - Q^(2) P `
` P^(2) (P-Q) = - Q^(2) (P-Q)`
`rArr (P^(2) +Q^(2)) (P-Q) = O`
`rArr abs((P^(2) +Q^(2)) (P-Q)) =abs(O)`
`rArr abs((P^(2) +Q^(2)))abs( (P-Q)) =0`
`rArr abs((P^(2) +Q^(2)))=0 " " [ because P ne Q]`
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ARIHANT MATHS ENGLISH-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
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  6. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

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  7. Let P and Q be 3xx3 matrices P ne Q. If P^(3)=Q^(3) and P^(2)Q=Q^(2)P,...

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  8. IF P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of 3xx3 matrix A and...

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

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

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  11. If A is an 3xx3 non-singular matrix such that A A^T=A^TA and B=A^(-1)A...

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

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

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  14. If A=[(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisying the equation A A...

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

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  16. If A=[(5a,-b),(3,2)] and A adj A=A A^(T), then 5a+b is equal to

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

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  18. Let z=(-1+sqrt(3)i)/(2), where i=sqrt(-1), and r, s in {1, 2, 3}. Let ...

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  19. Let P=[(1,0,0),(3,1,0),(9,3,1)] and Q = [q(ij)] be two 3xx3 matrices s...

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  20. If A=[(2,-3),(-4,1)], then adj (3A^(2)+12 A) is equal to

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