`|[a+b,a,b],[a,a+c,c],[b,c,b+c]|`is equal to

|{:(a,b,c),(b,c,a),(c,a,b):}| is equal to

|[a,a^(2),b+c],[b,b^(2),c+a],[c,c^(2),a+b]| is equal to

If the vectors a, b and c are coplanar, then |{:(a, b, c),(a*a, a*b,a*c),(b*a,b*b,b*c):}| is equal to

Let a, b, c be positive and not all equal. Show that the value of the determinant |[a,b,c],[b,c,a],[c,a,b]| is negative

If |[a+b,b+c,c+a],[c+a,a+b,b+c],[b+c,c+a,a+b]|=t X det of circulant matrix whose whose elemnts of the first column are a,b,c then t equals