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If A is an invertible matrix then which ...

If A is an invertible matrix then which of the following are true?

A

`A!=0`

B

`|A|!=0`

C

`adjA!=0`

D

`A^-1=|A|adjA`

Text Solution

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The correct Answer is:
`(A , B , C)`
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KC SINHA-MATRICES - FOR COMPETITION-Exercise
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  2. If A is an invertible matrix of order nxxn, (nge2), then (A) A is symm...

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  3. If A is an invertible matrix then which of the following are true?

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  4. If A and B are invertible matrices of the same order then (A) Adj(AB)=...

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  5. The system x+y+z=6, x+2y+3z=10, x+2y+lamdaz=gamma of simultaneous equa...

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  6. A square matrix A is said to be orthogonal if A^T A=I If A is a square...

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  7. A square matrix A is said to be orthogonal if A^T A=I If A is a square...

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  8. A square matrix A is said to be orthogonal if A^T A=I If A is a sqaure...

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  9. A square matrix A is said to be orthogonal if A^T A=I If A is a sqaure...

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  10. If A is a square matrix of any order then |A-x|=0 is called the charac...

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  11. If A is a square matrix of any order then |A-x|=0 is called the chract...

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  12. If A is a square matrix of any order then |A-x|=0 is called the charac...

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  13. If the matrix [(1,3,lamda+2),(2,4,8),(3,5,10)] is singular then find l...

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  14. If A=[(1,3),(3,4)] and A^2-xA-I=0 then find x.

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  15. For a 3xx3 matrix A if |A|=4, then find |AdjA|

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  16. Assertion: |M|=0, Reason: Determinant of a skew symmetric matrix is 0....

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  17. Assertion: |A A^T|=0, Reason : A is a skew symmetric matrix (A) Both A...

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  18. Assertion : A^-1 exists, Reason: |A|=0 (A) Both A and R are true and R...

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  19. Assertion: |AadjA|=-1, Reason : If A is a non singular square matrix o...

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  20. Assertion: adj A is a no singular matrix., Reason: A is a no singular ...

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