Using the property of determinants and without expanding ` {:[( 1,bc,a(a+c) ),(1,ca,b( c+a)) ,( 1,ab,c(a+b) )]:}=0`

Using the property of determinants and without expanding {:[( 0,a,-b),(-a,0,-c),( b,c,0) ]:}=0

Using the property of determinants and without expanding {:[( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)]:} =0

Using the property of determinants and without expanding {:[( x,a,x+a),( y,b,y+b),(z,c,z+c)]:} =0

Using the property of determinants and without expanding {:[( -a^(2) , ab,ac),( ba,-b^(2) , bc) ,( ca, cb, -c^(2)) ]:} =4a^(2) b^(2) c^(2)

Using the property of determinants and without expanding {:[( b+c,q+r,y+z),( c+a,r+p,z+x),( a+b,p+q,x+y) ]:}=2 {:[(a,p,x),( b,q,y),(c,r,z)]:}

By using properties of determinants , show that : {:[( a^(2) + 1, ab,ac),(ab,b^(2) + 1,bc),( ca, cb, c^(2) +1) ]:}= 1+a^(2) +b^(2) +c^(2)

By using properties of determinants , show that : (i) {:[( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))]:}=(a-b)(b-c) (c-a) (ii) {:[( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))]:} =( a-b) (b-c)( c-a) (a+b+c)

Using properties of determinants Prove that |{:(a+b+c,,-c,,-b),(-c,,a+b+c,,-a),( -b,,-a,,a+b+c):}| = 2 (a+b) (b+c) (c+a)

Evaluate Delta = {:[ (1,a,bc),( 1,b,ca),(1,c,ab)]:}

Using properties of determinants, prove that |(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)|=4a^2 b^2 c^2