Is the transpose of a singular matrix always singular?

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Thread starter PrathameshR
Start date May 1, 2017
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Matrices

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PrathameshR

Thread starter
May 1, 2017

Let's say A is a singular matrix. Will the transpose of this matrix be always singular? If so why?

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WubbaLubba Dubdub

May 1, 2017

Determinant of A is equal to the determinant of the transpose of A.
Since A is singular, det(A) = 0 which implies det(transpose of A) =0 and hence, transpose of A will also be a singular matrix.

Is the transpose of a singular matrix always singular?

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