Prove: `|((a+1)(a+2),(a+2),1 ),((a+2)(a+3),(a+3),1), ((a+3)(a+4) ,(a+4),1) |=-2`

Using properties of determinants, prove that |[(a+1)(a+2),a+2,1],[(a+2)(a+3),a+3,1],[(a+3)(a+4),a+4,1]|=-2

Prove: |(1,a, a^2),(a^2, 1,a),( a, a^2, 1)|=(a^3-1)^2

Locate the points: (1, 1), (1, 2), (1, 3), (1, 4) (2, 1), (2, 2), (2, 3), (2, 4) (1, 3), (2, 3), (3, 3), (4, 3) (1, 4), (2, 4), (3, 4), (4, 4)

Given A=[(5, 0, 4),( 2, 3, 2),( 1, 2, 1)] , B^(-1)=[(1, 3, 3),( 1, 4, 3),( 1, 3, 4)] . Compute (A B)^(-1) .

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

Let A = {1,2,3,4} and f : A to A satisfy f (1) =2, f(2)=3, f(3)=4, f (4)=1. Suppose g:A to A satisfies g (1) =3 and fog = gof , then g = (a).{(1,3), (2,1), (3,2), (4,4)} (b).{(1,3), (2,4),(3,1),(4,2)} (c).{(1,3),(2,2),(3,4),(4,3)} (d).{(1,3),(2,4),(3,2),(4,1)}

Let A={1,2,3,4} and R be a relation in given by R= (1,1), (2, 2), (3. 3). (4,4), (1,2), (2,1),(3,1), (1,3)} . Then R is

Let R = {(1, 2), (2, 2), (1, 1), (4,4), (1,3), (3, 3), (3,2)} be a relation on the set {1,2,3,4}. Then,

Evaluate the following: ([(1,3),( -1,-4))]+[(3 ,-2 ),(-1 ,1)]) [(1 ,3,5),( 2 ,4 ,6)]

Let R={(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation the set A= {1, 2, 3, 4} . The relation R is