If `A=[(ab ,b^2) ,(-a^2 ,-ab)]` , show that `A^2=O` .

If {:A=[(ab,b^2),(-a^2,-ab)]:} , then A is

If A=[[0 ,c,-b],[-c, 0, a],[ b, -a, 0]] and B=[[a^2, ab, ac],[ ab, b^2 , bc],[ ac ,bc, c^2]] , show that A B=B A=O_3xx3 .

If A=[{:(0," "c,-b),(-c," "0," "a),(b,-a," "0):}]" and "B=[{:(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2)):}] , show that AB is a zero matrix.

In a square ABCD, show that AC^(2) = 2AB^(2) .

If A=[{:(3,-1),(1,-3):}]" and B"=[{:(2,1),(-1,-2):}]," then show that" : (AB)^(-1)=B^(-1)A^(-1)

If A=[[1,2],[5,7]] and B=[[2,0],[ 3,-4]] , show that AB!=BA

If A=[[-1,2],[3,4]] and B=[[2,-3],[5,1]] show that AB!=BA

If "log" (a-b)/(2) = (1)/(2) (log a + log b), show that : a^(2) + b^(2) = 6ab .

(i) if A=[{:(1,-4),(3,1):}]and b=[{:(1,0,5),(-2,4,3):}], then show that : (AB)'=B'A' (ii) if A=[{:(2,3),(0,1):}]and B=[{:(3,4),(2,1):}], then prove that : (AB)'=B'A'

Add : 3ab^(2) , - 5ab^(2)