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Let Aa n dB be two 2xx2 matrices. Consid...

Let `Aa n dB` be two `2xx2` matrices. Consider the statements `A B=O A+OorB=O` `A B=I_2 A=B^(-1)` `(A+B)^2=A^2+2A B+B^2` (i) and (ii) are false, (iii) is true (ii) and (iii) are false, (i) is true (i) is false (ii) and, (iii) are true (i) and (iii) are false, (ii) is true

A

Is false (ii) and (iii) are true

B

(i) and (iii) are false (ii) is true

C

(i) and (ii) are false (iii) is true

D

(ii) and (iii) are false (i) is true

Text Solution

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The correct Answer is:
B
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FIITJEE-MATRICES -ASSIGNMENT PROBLEM (OBJECTIVE) (Level-I)
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  2. If I=[{:(,1,0),(,0,1):}], J=[{:(,0,1),(,-1,0):}]and B=[{:(,cos theta,s...

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  4. Let Aa n dB be two 2xx2 matrices. Consider the statements A B=O A+Oo...

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  5. The number of 3xx3 matrices with entries from the set {-1, 0,1} such t...

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  6. If A and B are symmetric matrices of order n(A!=B) then (A) A+B is ske...

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  7. The number of all the matrices A= [adj ]1le 1i,le 4 such that a(ij) =...

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  8. Let A =[(1,-1,1),(2,1,-3),(1,1,1)] and 10B=[(4,2,2),(-5,0,alpha),(...

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  10. If Aa n dB are square matrices of the same order and A is non-singular...

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  11. The inverse of a skew symmetric matrix is

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  12. If [{:( 1,2,3),(1,3,5),(1,5,12):}] then adj (adj A) is

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  13. Let A be a square matrix of order 3 such that transpose of inverse of ...

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  14. If A =[{:( alpha , a ),( beta , b),( gamma, c):}] then (A)A^(T) is

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  15. If A and B are non-singular square matrices of same order then adj(AB)...

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  17. If A =({:( 1,1,1),( 1,omega ^(2) , omega ),( 1 ,omega , omega ^(2)) :...

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  19. Statement -1 :if A = [a(ij) ](nxxn) and a(ij) =( i^(2) +j^(2) -ij) (I...

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  20. Statement 1: F a,b,c are real positive numbers with abc =1 and AA^(T) ...

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