[" Faffe tortwo qरofित Keiji "],[[" (1) "[[a,b],[-b,a]][[a,-b],[b,a]]]]

prove |[1, b c, a(b+c)],[ 1, c a, b(c+a)],[ 1, a b, c(a+b)]|=0

Show that |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0 .

If A = [[1,-1],[2,-1]],B = [[a,1],[b,-1]] and (A+B)^2 = A^2+B^2 find a and b.

If a=2 and b=3, then find the values of each of the following: (i) a^a+b^b (ii) a^b+b^a (iii) a^b (a/b)^a (iv) (1/a+1/b)^a

If A=[[a,b],[-1,2]],B=[[1,1],[2,4]] and (A+B)(A-B)=A^(2)-B^(2) , then the value of a+b equals

If A=[[1,-1],[ 2,-1]] and B=[[a,1],[b,-1]] and (A+B)^2=A^2+B^2, then find the value of a and b .

If A=[[1,-1],[2,-1]] , B=[[a,1],[b,-1]] and (A+B)^(2)=A^(2)+B^(2) ,then find the values of a and b

The value of |{:(1,1,1),(b+c,c+a,a+b),(b+c-a,c+a-b,a+b-c):}| is

Prove that the points (a ,\ b),\ (a_1,\ b_1) and (a-a_1,\ b-b_1) are collinear if a b_1=a_1b .

If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x is equal to [a , b , in (0,1)] (a)(a-b)/(1+a b) (b) b/(1+a b) (c) b/(1+a b) (d) (a+b)/(1-a b)