Construct the multiplication table `X_7` on the set {1, 2, 3, 4, 5, 6}. Also find the inverse element of 4 if it exists.

Construct the multiplication table xx_(7) on the set {1,2,3,4,5,6}. Also find the inverse element of 4 if it exists.

Construct the multiplication table times7 on the set {1, 2, 3, 4, 5, 6}. Also find the converse of 4 if exists.

Let Abe set of all cube roots of unity and let multiplication operation (x) be a binary operation on A. Construct the composition table for (x),on A. Also, find the identity element for (x) on A. Also, check its commutativity and prove that every element of A is invertible.

Construct the composition table/multiplication table for the binary operation * defined on {0, 1, 2, 3, 4, 5} given by a**b=ab (mod 6). Find the identity element if any. Also, find the inverse of elements 1 and 5.

Let us consider a binary operation ** on the set {1, 2, 3, 4, 5} given in the following table. Is ** commutative.

Let us consider a binary operation ** on the set {1, 2, 3, 4, 5} given in the following table. Compute (2**3)**(4**5) .

Find the direction cosines of the line (x + 2)/2 = (2y-7)/6 = (5 -z)/6 Also find the vector equation of the line passing through the point (-1, 2, 3) and parallel to the given line.

Constract the composition table/multiplication table for the binary operation * defined on {0,1,2,3,4}by a**b =axxb ("mod" =5) . Find the identity element if any. Also find the inverse elements of 2 and 4.

Find the inverse of the matrix [[1,2],[3,4]]