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 prove that {:|( 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 prove that {:|( 2,7,65),( 3,8,75),( 5,9,86) |:} = 0

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

Using the property of determinants and without expanding prove that {:|( -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)|:}

|(x, 4, y+z),(y, 4, z+x),(z, 4, x+y)|=

Without expanding prove that Delta ={:|( x+y,y+z,z+x) ,( z,x,y),( 1,1,1) |:} =0

Using Properties of determinants, prove that: {:|(x^2+1,xy,yz),(xy,y^2+1,yz),(xz,yz,z^2+1)|=1+x^2+y^2+z^2

Using Properties of determinants, prove that: {:|(b+c,c+a,a+b),(q+r,r+p,p+q),(y+z,z+x,x+y)|=2{:|(a,b,c),(p,q,r),(x,y,z)|