High School Singular Matrices: Transpose & Its Impact

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A singular matrix A has a determinant of zero, which means it cannot be inverted. The determinant of the transpose of A is equal to the determinant of A, so det(transpose of A) also equals zero. Therefore, the transpose of a singular matrix is always singular. This confirms that singularity is preserved under transposition. Understanding this property is crucial in linear algebra.
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Let's say A is a singular matrix. Will the transpose of this matrix be always singular? If so why?
 
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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.
 
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