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Add: `ab-4a,4b-ab,4a-4b`

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Add the following: ab-bc-ca , ca-ab

The determinant |(b^2-ab,b-c,-ac),(ab-a^2,a-b,b^2-ab),(bc-ac,c-a,ab-a^2)| equals :

Simplify combining like terms: 3a-2b-ab-(a-b+ab)+3ab+b-a

Add the following: a-b+ab , b-c+bc ,c-a+ac

If A= [[ab,b^2],[-a^2, -ab]] then A^(2)=

Prove that |(-a^2,ab,ac),(bc,-b^2,bc),(ca,cb,-c^2)|=4a^(2)b^(2) c^(2) .

If abs(a + b) = abs(a-b) then

Using the Properties of determinants, prove that following: {:|(-a^2,ab,ac),(ba,-b^2,bc),(ac,bc,-c^2)|=4a^2b^2c^2

Using the property of determinants and without expanding prove that {:|( -a^(2) , ab,ac),( ba,-b^(2) , bc) ,( ca, cb, -c^(2)) |:} =4a^(2) b^(2) c^(2)

Let Delta=|(a,a+b,a+b+c),(3a,4a+3b,5a+4b+3c),(6a,9a+6b,11a+9b+6c)| where a=i, b=omega,c = omega^2 , then Delta is equal to