Prove without expansion that `|(ah+bg, g, ab+ch) (bf+ba, f, hb+bc) (af+bc, c , bg+fc)|=a|(ah+bg ,a, h) (bf+ba, h, b) (af+bc, g, f)|`

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)) ]:}

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):}|

If U = { a, b, c, d, e, f, g, h} , find the complements of the following sets : C = {a, c, e, g}

If U = { a, b, c, d, e, f, g, h} , find the complements of the following sets : B = {d, e, f, g}

If U = { a, b, c, d, e, f, g, h} , find the complements of the following sets : A = {a, b, c}

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2):}|=4a^2b^2c^2

If U = { a, b, c, d, e, f, g, h} , find the complements of the following sets : D = { f, g, h, a}

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)):}|=0