If `A B=Aa n dB A=B ,` then a. `A^2B=A^2` b. `B^2A=B^2` c. `A B A=A` d. `B A B=B`

If Aa n dB are two matrices such that A B=Ba n dB A=A ,t h e n (A^5-B^5)^3=A-B b. (A^5-B^5)^3=A^3-B^3 c. A-B is idempotent d. none of these

If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n dY=A B-B A ,t h e n(X Y)^T is equal to X Y b. Y X c. -Y X d. none of these

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then (a) 3b^2=a^2-c (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

If Aa n dB are square matrices of the same order and A is non-singular, then for a positive integer n ,(A^(-1)B A)^n is equal to A^(-n)B^n A^n b. A^n B^n A^(-n) c. A^(-1)B^n A^ d. n(A^(-1)B^A)^

If sin theta + cos theta = a, and sin theta = cos theta = b , then A) a^2 + b^2 = 1 B) a^2 - b^2 = 1 C) a^2 + b^2 = 2 D) a^2 - b^2 = 2

a ,b ,c x in R^+ such that a ,b ,a n dc are in A.P. and b ,ca n dd are in H.P., then a b=c d b. a c=b d c. b c=a d d. none of these

if Aa n dB are squares matrices such that A^(2006)=Oa n dA B=A+B ,t h e n"det"(B) equals 0 b. 1 c. -1 d. none of these

Let Aa n dB be two 2xx2 matrices. Consider the statements (i) A B=O, A=O or B=O (ii) A B=I_2 implies A=B^(-1) (iii) (A+B)^2=A^2+2A B+B^2 a. (i) and (ii) are false, (iii) is true b. (ii) and (iii) are false, (i) is true c. (i) is false (ii) and, (iii) are true d. (i) and (iii) are false, (ii) is true

In an acute triangle A B C if sides a , b are constants and the base angles Aa n dB vary, then show that (d A)/(sqrt(a^2-b^2sin^2A))=(d B)/(sqrt(b^2-a^2sin^2B))

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2, B=b^2c+b c^2-a^2b-a b^2, and C=a^2c+a c^2-b^2c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot