Using properties of determinants, prove that `|(a^2+2a, 2a+1,1), (2a+1, a+2, 1), (3,3,1)| = (a-1)^3`

Using properties of determinant, prove that |{:(a^(2)+2a, 2a+1, 1), (2a+1, a+2, 1), (3, 3, 1):}|=(a-1)^(3)

Using properties of determinants, prove that 3 2 (a 1) 3 3 1 2a 1 a 2 1 a 2a 2a

Show that |{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}|=(a-1)^3

Using properties of determinants,prove that det[[a^(2)+2a,2a+1,12a+1,a+2,13,3,1]]=(a-1)^(3)

Using the proprties of determinants in Exercise 7 to 9, prove that |{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}|=(a-1)^3

Using properties of determinant prove that |(a^(2)+1, ab, ac),(ab, b^(2)+1, bc),(ca, cb,c^(2)+1)|=(1+a^(2)+b^(2)+c^(2)) .

Using properties of determinant, prove that |{:( 1,a,a^(2)),(a^(2) , 1,a),( a,a^(2),1):}|=(a^(3) -1)^(2)

Using properties of determinants prove that |(1,1, 1+3x),(1+3y,1,1),(1, 1+3z,1)| =9(3xyz+xy+yz+zx)