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Which of the following statements is not correct for a square matrix A? (| A | ≠ 0)

  • a)
    If A is a diagonal matrix, A-1 will also be a diagonal matrix

  • b)
    If A is a symmetric matrix, A-1 will be a symmetric matrix

  • c)
    If A–1 = A ⇒ A is an idempotent matrix

  • d)
    If A–1 = A ⇒ A is an involutary matrix

Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Which of the following statements is not correct for a square matrix A...
if we get A2 = I →then it's know as  Involuntary Matrix
if we get A2 = A → then matrix is Idempotent Matrix
and
If A is a symmetric matrix, A-1 will also be a symmetric matrix
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Which of the following statements is not correct for a square matrix A? (| A | ≠ 0)a)If A is a diagonal matrix, A-1will also be a diagonal matrixb)If A is a symmetric matrix, A-1will be a symmetric matrixc)If A–1= A ⇒ A is an idempotent matrixd)If A–1= A ⇒ A is an involutary matrixCorrect answer is option 'C'. Can you explain this answer?
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Which of the following statements is not correct for a square matrix A? (| A | ≠ 0)a)If A is a diagonal matrix, A-1will also be a diagonal matrixb)If A is a symmetric matrix, A-1will be a symmetric matrixc)If A–1= A ⇒ A is an idempotent matrixd)If A–1= A ⇒ A is an involutary matrixCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Which of the following statements is not correct for a square matrix A? (| A | ≠ 0)a)If A is a diagonal matrix, A-1will also be a diagonal matrixb)If A is a symmetric matrix, A-1will be a symmetric matrixc)If A–1= A ⇒ A is an idempotent matrixd)If A–1= A ⇒ A is an involutary matrixCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is not correct for a square matrix A? (| A | ≠ 0)a)If A is a diagonal matrix, A-1will also be a diagonal matrixb)If A is a symmetric matrix, A-1will be a symmetric matrixc)If A–1= A ⇒ A is an idempotent matrixd)If A–1= A ⇒ A is an involutary matrixCorrect answer is option 'C'. Can you explain this answer?.
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