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 B is an idempotent matrix, and A=I-B , then a. A^2=A b. A^2=I c. A B=O d. B A=O

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 A and B are two square matrices such that B=-A^(-1)B A ,t h e n(A+B)^2 is equal to a. A^2+B^2 b. O c. A^2+2A B+B^2 d. A+B

If A B=Aa n dB A=B , then which of the following is/are true? A is idempotent b. B is idempotent c. A^T is idempotent d. none of these

If A=[[1,-1],[ 2, 1]],B=[[a,1],[b,-1]]a n d(A+B)^2=A^2+B^2+2A B ,t h e n a. a=-1 b. a=1 c. b=2 d. b=-2

if a:b = b:c prove that ((a+b)/(b+c))^2 = (a^2+b^2)/(b^2+c^2) .

If Aa n dB are two events such that P(A)=1/2a n dP(B)=2/3 . Then show that P(A U B) ge 2/3 .

If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=a b b. a^2+c^2=-a b c. a^2-c^2=-a b d. none of these

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 - bc^2, and C=a^2c +'a c^2-b^2' c-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

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 3b^2=a^2-c ^2 (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2