IIT JAM Exam  >  IIT JAM Questions  >  Which of the following statements is/are inco... Start Learning for Free
Which of the following statements is/are incorrect?
(i) Adjoint of a symmetric matrix is symmetric.     
(ii) Adjoint of a unit matrix is a unit matrix. 
(iii) A (adj a) = (adj A) A = |A|             
(iv) Adjoint of a diagonal matrix is a diagonal matrix. 
  • a)
    (i)
  • b)
    (ii)
  • c)
    (iii) and (iv)
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which of the following statements is/are incorrect?(i) Adjoint of a sy...
d) None of these All of the statements are correct.
(i) Adjoint of a symmetric matrix is symmetric. This is true because the adjoint of any matrix is the transpose of its conjugate,and if the matrix is symmetric, its transpose is the same as its conjugate.
(ii) Adjoint of a unit matrix is a unit matrix.This is true because the adjoint of a unit matrix is simply its transpose, which is also a unit matrix.
(iii) A(adja) (adjA)A=|A|.This is true because the adjoint of any matrix is the transpose of its conjugate,so A(adja)=(adjA) A= the transpose of the conjugate of A times A,which is equal to the determinant of A.
(iv) Adjoint of a diagonal matrix is adiagonal matrix. This is also true because the adjoint of a diagonal matrix is simply its transpose, which is also diagonal.
View all questions of this test
Most Upvoted Answer
Which of the following statements is/are incorrect?(i) Adjoint of a sy...
Incorrect Statements about Adjoint Matrix

Statement: Adjoint of a symmetric matrix is symmetric.

Incorrect

Explanation: The adjoint matrix, also known as the adjugate or classical adjoint, of a matrix A is the transpose of its cofactor matrix. The adjoint of a symmetric matrix may or may not be symmetric.

Statement: Adjoint of a unit matrix is a unit matrix.

Incorrect

Explanation: The adjoint of a unit matrix is not necessarily a unit matrix. The adjoint of a matrix A is defined as the transpose of its cofactor matrix, which depends on the elements of A.

Statement: A (adj A) = (adj A) A = |A|

Incorrect

Explanation: The correct statement is A(adj A) = (adj A)A = |A|I, where I is the identity matrix.

Statement: Adjoint of a diagonal matrix is a diagonal matrix.

Incorrect

Explanation: The adjoint of a diagonal matrix is not necessarily a diagonal matrix. The adjoint matrix is obtained by taking the transpose of the cofactor matrix of the original matrix, which may not preserve the diagonal structure of the matrix.
Free Test
Community Answer
Which of the following statements is/are incorrect?(i) Adjoint of a sy...
Explore Courses for IIT JAM exam
Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer?
Question Description
Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for IIT JAM. Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free.
Here you can find the meaning of Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice IIT JAM tests.
Explore Courses for IIT JAM exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev