Consider the following statements regarding Eigenvalues:S1: Eigenvalues of A and A-1 are the same.S2: Eigenvalues of A and AT are the same.S3: If A is a singular matrix, then at least one of its Eigenvalue is 0.Which option is correct?a)Only S2 is correctb)S1 and S3 are correctc)S2 and S3 are correctd)S1 and S2 are correctCorrect answer is option 'C'. Can you explain this answer?

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Consider the following statements regarding Eigenvalues:

S1: Eigenvalues of A and A-1 are the same.

S2: Eigenvalues of A and AT are the same.

S3: If A is a singular matrix, then at least one of its Eigenvalue is 0.

Which option is correct?

a)
Only S2 is correct
b)
S1 and S3 are correct
c)
S2 and S3 are correct
d)
S1 and S2 are correct

Correct answer is option 'C'. Can you explain this answer?

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Consider the following statements regarding Eigenvalues:S1: Eigenvalu...

S1: The Eigenvalues of A 1 are the reciprocal of Eigenvalues of A, Hence False

S2: The Eigenvalues of AT are the same as of Eigenvalues of A, Hence True

S3: If A is singular matrix, then |A| = 0. As the determinant is given by the product of Eigenvalues, hence for the product to be 0, at least one of the Eigenvalue must be 0.

Hence S2 and S3 are correct.

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Consider the following statements regarding Eigenvalues:S1: Eigenvalues of A and A-1 are the same.S2: Eigenvalues of A and AT are the same.S3: If A is a singular matrix, then at least one of its Eigenvalue is 0.Which option is correct?a)Only S2 is correctb)S1 and S3 are correctc)S2 and S3 are correctd)S1 and S2 are correctCorrect answer is option 'C'. Can you explain this answer?

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