If A is skew-symmetric matrix of order `2 and B=[(1,4),(2,9)] and c[(9,-4),(-2,1)]` respectively. Then `A^3 BC + A^5B^2C^2 + A^7B^3C^3 +.....+A^(2n+1) B^n C^n` where `n in N` is

If A is a skew-symmetric matrix of order 2 and B, C are matrices [[1,4],[2,9]],[[9,-4],[-2,1]] respectively, then A^(3) (BC) + A^(5) (B^(2)C^(2)) + A^(7) (B^(3) C^(3)) + ... + A^(2n+1) (B^(n) C^(n)), is

If A is a skew-symmetric matrix of order 2 and B, C are matrices [[1,4],[2,9]],[[9,-4],[-2,1]] respectively, then A^(3) (BC) + A^(5) (B^(2)C^(2)) + A^(7) (B^(3) C^(3)) + ... + A^(2n+1) (B^(n) C^(n)), is

Prove that C_3 + 2.C_4+ 3.C_5 + ……..+ (n-2).C_n = (n-4).2^(n-1) + (n+2) where n > 3

Show that C_2 + 2C_3 + 3C_4 + ... + (n-1)C_n = 1+ (n-2) 2^(n-1)

If A,B and C are n xx n matrix and det (A) = 2, det (B)= 3, and det (C ) = 5, then find the value of the det (A^(2) BC^(-1)) .

If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3)] , then A B is equal to (A) B (B) n B (C) B^n (D) A+B

If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3)] , then A B is equal to (A) B (B) n B (C) B^n (D) A+B

If there are three square matrix A, B, C of same order satisfying the equation A^2=A^-1 and B=A^(2^n) and C=A^(2^((n-2)) , then prove that det .(B-C) = 0, n in N .

If there are three square matrix A, B, C of same order satisfying the equation A^2=A^-1 and B=A^(2^n) and C=A^(2^((n-2)) , then prove that det .(B-C) = 0, n in N .