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Prove that: |1a a^2-b c1bb^2-c a1cc^2-a ...

Prove that: `|1a a^2-b c1bb^2-c a1cc^2-a b|=0`

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Using the property of determinants and without expanding, prove that: |-a^2a b a c b a b^2b cc a c b-c^2|=4a^2b^2c^2

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If a, b and c are in G.P. then prove that 1 a 2 - b 2 + 1 b 2 = 1 b 2 - c 2 . 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

Without expanding at any stage, prove that |{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|=|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

Using the property of determinants and without expanding, prove that: |1b c a(b+c)1c a b(c+a)1a b x(a+b)|=0

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  3. Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

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