If `a, b, c, d in R` and `A=[(a,b),(c,d)]` , show that `A^2-(a+d)A+(ad-bc)I` is a null matrix.

If a, b, c are in A.P. and a,b, d are in G.P., prove that a, a-b, d-c are in G.P.

If frac(a)(b) = frac(c ) (d) , show tha ad = bc

If a,b,c,d are in G.P then show that (b-c)^2+(c-a)^2+(d-b)^2=(a-d)^2 .

Give examples to show that : A^2 is a null matrix though A is not null matrix.

If frac(a)(b) = frac(c )(d) , show that frac(a+b)(b) = frac(c+d)(d)

Let N be the set of all natural numbers and R be the relation in NxxN defined by (a,b) R (c,d), if ad=bc. Show that R is an equivalence relation.

Given that the universal set U = {a, b, c, d, e, f, g, h} and A = {a, b, c, d, e}, B = {a, c, e, g), C= {b, c, f, g} then determine (A-B)-C

Given that the universal set U = {a, b, c, d, e, f, g, h} and A = {a, b, c, d, e}, B = {a, c, e, g), C= {b, c, f, g} then determine A-(B-C)

Given that the universal set U = {a, b, c, d, e, f, g, h} and A = {a, b, c, d, e}, B = {a, c, e, g), C= {b, c, f, g} then determine AnnBnnC