Using the properties of determinants,prove |3a,-a+b,-a+c||a-b,3b,c-b||a-c,b-c,3c|=3(a+b+c)(ab+bc+ca)

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|{:( 3a, -a+b,-a+c),(a-b,3b, c-b),(a-c,b-c, 3c):}|=3(a+b+c)(ab+bc+ca) | 12 | DETERMINANT | MATH... |{:( 3a, -a+b,-a+c),(a-b,3b, c-b),(a-c,b-c, 3c):}|=3(a+b+c)(ab+bc+ca) | 12 | DETERMINANT | MATH...
determinant (3a -a+b -a+c , -b+a 3b -b+c , -c+a -c+b 3c) = 3(a+b+c)(ab+bc+ca) determinant (3a -a+b -a+c , -b+a 3b -b+c , -c+a -c+b 3c) = 3(a+b+c)(ab+bc+ca)
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