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Which of the following statement is false?
  • a)
    Every skew symmetric matrix of odd order is non-singular
  • b)
    If the determinant of a square matrix is non zero, then matrix is non-singular
  • c)
    The adjoint symmetric matrix of symmetric matrix is symmetric
  • d)
    The adjoint matrix of a diagonal matrix is diagonal
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which of the following statement is false?a)Every skew symmetric matri...
The determinant of skew-symmetric matrix of odd order is always zero
Therefore the inverse of skew-symmetric matrix does not exist
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Most Upvoted Answer
Which of the following statement is false?a)Every skew symmetric matri...
Every skew symmetric matrix of an odd order is singular or its determinant will be equal to zero.
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Community Answer
Which of the following statement is false?a)Every skew symmetric matri...
The statement "Every skew symmetric matrix of odd order is non-singular" is false.

Skew Symmetric Matrix:
A skew symmetric matrix is a square matrix in which the transpose of the matrix is equal to the negative of the matrix itself. In other words, for a skew symmetric matrix A, A^T = -A.

Non-Singular Matrix:
A non-singular matrix is a square matrix that has an inverse. In other words, if A is a non-singular matrix, there exists a matrix B such that AB = BA = I, where I is the identity matrix.

Explanation:

To prove that the statement is false, we need to provide a counterexample.

Counterexample:

Let's consider a 3x3 skew symmetric matrix A as follows:

A = [0 1 0]
[-1 0 0]
[0 0 0]

Now, let's find the determinant of matrix A.

det(A) = (0 * 0 * 0) + (1 * 0 * 0) + (0 * (-1) * 0) - (0 * 0 * (-1)) - (1 * 0 * 0) - (0 * 0 * 0) = 0

Since the determinant of matrix A is zero, we can conclude that matrix A is singular. Therefore, the statement "Every skew symmetric matrix of odd order is non-singular" is false.

In this counterexample, we have shown that a skew symmetric matrix of odd order can indeed be singular.

Conclusion:

The false statement is that every skew symmetric matrix of odd order is non-singular. We have provided a counterexample to demonstrate that this statement does not hold true.
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Which of the following statement is false?a)Every skew symmetric matrix of odd order is non-singularb)If the determinant of a square matrix is non zero, then matrix is non-singularc)The adjoint symmetric matrix of symmetric matrix is symmetricd)The adjoint matrix of a diagonal matrix is diagonalCorrect answer is option 'A'. Can you explain this answer?
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Which of the following statement is false?a)Every skew symmetric matrix of odd order is non-singularb)If the determinant of a square matrix is non zero, then matrix is non-singularc)The adjoint symmetric matrix of symmetric matrix is symmetricd)The adjoint matrix of a diagonal matrix is diagonalCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Which of the following statement is false?a)Every skew symmetric matrix of odd order is non-singularb)If the determinant of a square matrix is non zero, then matrix is non-singularc)The adjoint symmetric matrix of symmetric matrix is symmetricd)The adjoint matrix of a diagonal matrix is diagonalCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statement is false?a)Every skew symmetric matrix of odd order is non-singularb)If the determinant of a square matrix is non zero, then matrix is non-singularc)The adjoint symmetric matrix of symmetric matrix is symmetricd)The adjoint matrix of a diagonal matrix is diagonalCorrect answer is option 'A'. Can you explain this answer?.
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