one of the properties of determinant is Interchanging two columns(rows) of a matrix will lead to change in the sign of determinant. does it also holds for interchanging its entries' sign will change the sign of the result? how? please help me.
2026-04-04 14:19:16.1775312356
changing the signs of the entries of $n \times n$ matrix from +(-) to -(+),respectively. Will change the signs of the determinant.
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Hint:
$\det(cA)=c^{n}\det(A),$ for an $n × n$ matrix $A$