Using properties of determinant show that`|(a+b,a,b),(a,a+c,c),(b,c,b+c)|=4abc`

Without expanding determinant show that |(0,a,b),(-a,0,c),(-b,-c,0)|=0

Without expanding the determinants,show that |(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c)|=3abc-a^3-b^3-c^3

Without expanding determinant show that |(b+c,bc,b^2c^2),(c+a,ca,c^2a^2),(a+b,ab,a^2b^2\)|=0

Select the correct options from the given alternatives.The determinant D=|(a,b,a+b),(b,c,b+c),(a+b,b+c,0)|=0 .If

Without expanding evaluate the following determinants. |(1,a,b+c),(1,b,c+a),(1,c,a+b)|

Select and write the correct answer from the given alternatives in each of the following: |(a+b,a,b),(a,c+a,c),(b,c,c+b)| is equal to

Without expanding,show that the values of the following determinants are zero: |(x,y,z),(x+3a,y+3b,z+3c),(a,b,c)|

Without expanding,show that the values of the following determinants are zero: |(a,b,c),(2,5,7),(a+4,b+10,c+14)|