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Let P and Q be two 2xx2 matrices. Consid...

Let P and Q be two `2xx2` matrices. Consider the statements
(i)`PQ=OimpliesO` or `Q=O` or both
(ii) `PQ=I_(2)impliesP=Q^(-1)`
(iii) `(P+Q)^(2)=P^(2)+2PQ+Q^(2)`. Then

A

I and ii are false while iii is true

B

I and iii are false while ii is true

C

ii and iii are false while I is true

D

none

Text Solution

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1C MCQ (INVERSE MATRIX)
  1. If A=[(1,3,3),(1,3,4),(1,4,3)] then A has

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  2. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

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  3. Let P and Q be two 2xx2 matrices. Consider the statements (i)PQ=Oimp...

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  4. Let P and Q be 3xx3 matrices with P!=Q. If P^(3)=Q^(3) and P^(2)Q=Q^(2...

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  5. Let A be a square matrix all of whose entries are integers. Then which...

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  6. Let A=((0,0,-1),(0,-1,0),(-1,0,0)). The only correct statement about t...

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  7. [(1,2,3),(2,5,7),(-2,-4,-5)] is the inverse of

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  8. If A=[(1,-2,3),(0,-1,4),(-2,2,1)] then (A^(T))=

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  9. If [(1,0,0),(-1,1,0),(-1,0,1)] is the inverse of [(1,0,0),(1,1,0),(1,0...

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  10. If A=[(0,1,2),(1,2,3),(3,1,1)] and A^(-1)=[(1//2,-1//2,1//2),(-4,3,x),...

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

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  12. If A=[(0,1,-1),(2,1,3),(3,2,1)] then [A(adjA)A^(-1)]A=

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  13. If A=[(cos alpha, - sin alpha, 0),(sin alpha, cos alpha, 0),(0,0,1)] t...

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  14. If A=[(1,1,1),(2,4,1),(2,3,1)],B=[(2,3),(3,4)] then the matrix BA is

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  15. If S=[(0,1,1),(1,1,1),(1,1,0)],then det of s

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  16. If A=I is 2x2 matrix then det(I+A)=

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  17. If A is a nonzero square matrix of order n with det(I+A)!=0 and A^(3)=...

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  18. If A!=I is an idempotent matrix, then A is a

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  19. If A is a singular matrix then adj A is

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  20. If A is an invertible matrix of order n, then the determinant of adj A...

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