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Which of the following is incorrect?...

Which of the following is incorrect?

A

`(A^(T))^(T)=A`

B

`A^(2)-B^(2)=(A+B)(A-B)`

C

`(A-I)(I+A)=O implies A^(2)=I`

D

`(AB)^(n)=A^(n)B^(n)`, where A, B commute

Text Solution

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The correct Answer is:
B
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NIKITA PUBLICATION-MATRICES-MULTIPLE CHOICE QUESTIONS
  1. If A and B are square matrices of order ntimesn, then (A-B)^(2)=

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  2. If A, B are two matrices and (A+B)(A-B)=A^(2)-B^(2), then

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  3. Which of the following is incorrect?

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  4. If A^(T), B^(T) are transpose of the square matrices A, B respectively...

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  5. Which of the following relations is incorrect?

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  6. Which one of the following statements is true?

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  7. If A=[[a(11), a(12), a(13)], [a(21), a(22), a(23)], [a(31), a(32), a(3...

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  8. If A=[[1, 1, 0], [2, 1, 5],[1, 2, 1]] and a(ij) denote the cofactor ...

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  9. If A=[[a(11), a(12), a(13)], [a(21), a(22), a(23)], [a(31), a(32), a(3...

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

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  11. If A is a non-singular matrix of order n, then A(adj A)=

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  12. If A is a singular matrix of order n, then A(adjA)=

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  13. If A is a ntimesn matrix and |A|ne0, then adj(adjA)=

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  14. If A is a singular matrix of order n, then (adjA) is

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  15. If A is a square matrix, then adj(A')-(adjA)'=

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  16. If A is a non-singular matrix of order 3, (adjA)+A^(-1)=0, then |A|=

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  17. If A is a non-singular matrix of order 3, then |adjA^(3)|=

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  18. If D is the determinant of a square matrix A of order n, then the dete...

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  19. Which of the following is/are incorrect? (i).Adjoint of symmetric mat...

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  20. The inverse of a matrix A=[[a, b], [c, d]] is

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