Prove that AB||CD if A = (-1,-2), B = (0, 1), C = (3, 0), D = (2, -3)

Prove that AB bot CD if A = (2, 1), B = (0, -1), C= (-1, 8), D = (4, 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 (AB)^(-1) = B^(-1) . A^(-1) give that A = [(2,3),(1,-4)] and B = [(1,-2),(-1,3)] .

Find AB, if A=[(0,-1),(0,2)] and B=[(3,5),(0,0)] .

The area of the quadrilateral ABCD, where A (0, 4, 1), B (2, 3, - 1), C(4, 5, 6) and D (2, 6, 2) is equal to :

If A = [{:(1,2),(-2,3):}], B= [{:(2,1),(2,3):}] and C = [{:(-3,1),(2,0):}] ,verify that (AB)C = A(BC) and A(B+C)=AB+AC.

If A = [(1,-1),(2,3)], B = [(1,3),(-1,4)] and C = [(2,-2),(3,0)] verify that A(BC) = (AB)C .

Prove that the points A(0,-1),B(-2,3),C(6,7) and D(8,3) are the vertices of a rectangle ABCD .

If A = [(4,-1),(0,3)], B = [(1,2),(-1,3)] and C = [(1, -2),(3,5)] verify that A(BC) = (AB)C .