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Using the property of determinants and without expanding, prove that:`|[0,a,-b],[-a,0,-c],[ b, c,0]|=0`

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`D= |[0,a,-b],[-a,0,-c],[b,c,0]|`
We know, if we interchange rows and columns of a determinant, value of the determinant does not change.
So, if we interchange rows and columns of given determinant, then,
`D = |[0,-a,b],[a,0,c],[-b,-c,0]| = (-1)^3|[0,a,-b],[-a,0,-c],[b,c,0]| = -D`
`:. D = -D`
`=>2D = 0`
`=> D = 0`
Therefore, value of the given determinant is `0`.
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