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Does a singular matrix have an adjoint matrix? My lecturer said that there is an adjoint matrix for every matrices be it singular or invertible. But I don't see how I can derive an adjoint matrix from a singular matrix?

Mathematics
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Yes. Just because the determinant is zero doesn't mean the matrix and its adjoint can't be computed. Just flip every other sign and transpose.
http://en.wikipedia.org/wiki/Adjugate_matrix
oh...so a singular square matrix is still possible to have an adjoint matrix. But will a singular rectangular matrix be able to have an adjoint matrix?

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