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

Show that the points (0, -1, 0), (2,1,-1), (1,1,1), (3,3,0) are coplanar.

Show that the matrix A=[{:(1,2,1),(3,2,3),(1,1,2):}] is non-singular and find A^-1 .

Show that the points (0,-1,0),(2,1,-1),(1,1,1),(3,3,0) are coplanar.

Show that the points (1, 2, 3), (2, 3, 1) and (3, 2, 1) form an equilateral triangle.

Show that (i) [(5,-1),(6,7)][(2,1),(3,4)] ne [(2,1),(3,4)][(5,-1),(6,7)] (ii) [(1,2,3),(0,1,0),(1,1,0)][(-1,1,0),(0,-1,1),(2,3,4)] ne [(-1,1,0),(0,-1,1),(2,3,4)][(1,2,3),(0,1,0),(1,1,0)]

Show that the points (4,7,8), (2,3,4) and (-1,-2,1),(1,2,5) are vertices of a parallelogram.

Find the product [{:(2,2,1),(1,0,2),(2,1,2):}][{:(-2,-3,4),(2,2,-3),(1,2,-2):}]

Show that the matrix A = [(1,2,1),(3,2,3),(1,1,2)] is non-singular and find A^(-1) .