Without expanding the determinant, show that the determinant `|{:(a^2+10,ab,ac),(ab,b^2+10,bc),(ac,bc,c^2+10):}|` is divisible by 100.

Show that, |{:(a^2+10,ab,ac),(ab,b^2+10,bc),(ca,bc,c^2+10):}| is divisible by 100 .

|{:(a^2,ab,ac),(ab,b^2,bc),(ca,bc,c^2):}|= ?

the determinant Delta=|[a^2+x, ab, ac] , [ab, b^2+x, bc] , [ac, bc, c^2+x]| is divisible by

Show that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ca,bc,c^(2)+1):}|=1+a^(2)+b^(2)+c^(2)

|{:(0,ab^2,ac^2),(a^2b,0,bc^2),(a^2c,cb^2,0):}|=2a^3b^3c^3

Without expanding the determinant, prove that {:|( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) |:} ={:|( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) |:}

Prove that, abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)) =1+ a^2+b^2+c^2 .

The value of the determinant |((1)/(a),1,bc),((1)/(b),1,ca),((1)/(c),1,ab)| is -

Prove that, abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)) =4 a^2b^2c^2 .

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)