Show that `|{:(a-b-c," "2a," "2a),(" "2b,b-c-a," "2b),(" "2c," "2c,c-a-b):}|=(a+b+c)^(3)`

By using properties of determinants , show that : (i) {:|( a-b-c, 2a, 2a),( 2b, b-c-a, 2b ) , ( 2c,2c, c-a-b) |:} = ( a+b+c)^(3) (ii) {:|( x+y+2z, x,y ),( z, y+z+2x, y ),( z,x,z+x+2y )|:} =2( x+y+z)^(3)

Prove that |{:(a-b-c, 2a, 2a), (2b, b-c-a, 2b), (2c, 2c, c-a-b):}|=(a+b+c)^(3)

prove that, |{:(" "2a,a-b-c," "2a),(" "2b," "2b,b-c-a),(c-a-b," "2c," "2c):}|=(a+b+c)^3

|{:(a+b+2c," "a," "b),(" "c,b+c+2a," "b),(" "c," "a,c+a+2b):}|=2(a+b+c)^3

Show that , |{:((a^2+b^2)/c," "c," "c),(" "a,(b^2+c^2)/a," "a),(" "b," "b,(c^2+a^2)/b):}|=4abc

prove that [ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]] = (a+b+c)^3

prove that [ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]] = (a+b+c)^3

prove that [ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]]= (a+b+c)^3

prove that [ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]] = (a+b+c)^3