Home
Class 12
MATHS
Let P and Q be 3 xx3 matrices with P !=...

Let P and Q be `3 xx3` matrices with `P != Q ` . If `P^(3) = Q^(3) and P^(2) Q = 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]`
Promotional Banner

Similar Questions

Explore conceptually related problems

If 80 = 2^(P) xx 5^(q) , then p + q =

If P = (0,1,2) and Q = (4,-2,1), O = (0,0,0) then P hat O Q =

Negation of (p to q) ^^ (q ^^ p) is

If z=x-iy , z^((1)/(2)=p+iq , then : ((x)/(p)+(y)/(q))//(p^(2),q^(2)) is equal to:

The negation of (p to q) ∨ (p to r) is

If p and q are positive real number such that p^(2) + q^(2) = 1 , then the maximum value of (p + q) is :

If x^(2)-3 x+2 is a factor of x^(4)-p x^(2)+q , then the values of p and q are

If P = [(((sqrt(3))/2,1/2),(1/2)),(((-1)/2),(sqrt(3))/2)] and A = [(1,1),(0,1)] and Q = PAP^(T), then P^(T) Q^(2005) P is equal to :

In the p^(th) term of an A.P. is q and q^(th) term is p, prove that the n^(th) term is equal to p+q-n.

If 3p^(2) = 5p + 2 and 3q^(2) = 5q + 2, where p ne q , then the equation whose roots are 3p - 2q and 3q - 2p is :