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Let A be a square matrix all of whose en...

Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

A

If `detA=!+1`, then `A^(-1)` exists and all its entries are no integers.

B

If det `A=+-1,` then `A^(-1)` exists and all its entries are integers

C

If det `A=+11`, then `A^(-1)` need not exist.

D

If det`A=+-1`, then `A^(-1)` exists but all its entries are not necessarily integers.

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

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

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

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

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

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  7. 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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  8. 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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  9. 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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  10. If A=[(0,1,-1),(2,1,3),(3,2,1)] then [A(adjA)A^(-1)]A=

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

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

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

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

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

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

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

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  19. If A is a nonsingular matrix of type n Adj(AdjA)=kA, then k=

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  20. If is a nonsingular matrix of type n then Adj(AdjA)=

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