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

Explanation

`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`.