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 A B=A and B A=B , where A and B are square matrices, then B^2=B and A^2=A (b) B^2!=B and A^2=A (c) A^2!=A , B^2=B (d) A^2!=A , B^2!=B

In an equilateral triangle A B C , if A D_|_B C , then (a) 2\ A B^2=3\ A D^2 (b) 4\ A B^2=3\ A D^2 (c) 3\ A B^2=4\ A D^2 (d) 3\ A B^2=2\ A D^2

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

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

Let A and B are square matrices of same order satisfying A B=A ,a n dB A=B , then (A^(2015)+B^(2015))^(2016) is equal to 2^(2015)(A^3+B^3) (b) 2^(2016)(A^2+B^2) 2^(2016)(A^3+B^3) (d) 2^(2015)(A+B)

If A and B are square matrices of the same order, then (A+B)(A-B) is equal to A^2-B^2 (b) A^2-B A-A B-B^2 (c) A^2-B^2+B A-A B (d) A^2-B A+B^2+A B

If A B=A ,B A=B then (A+B)^n= (where n in N) (1) (A^2+B^2) (2) (A+B) (3) 2^(n-1)(A+B) (4) 2^n(A+B)

In Figure, A D_|_B C and B D=1/3C Ddot Prove that 2C A^2=2A B^2+B C^2

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