Statement 1: If `A ,B ,C` are matrices such that `|A_(3xx3)|=3,|B_(3xx3)|=-1,a n d|C_(2xx2)|=_2, t h e n|2A B C|=-12.` Statement 2: For matrices `A ,B ,C` of the same order,`|A B C|=A=|A||B||C|dot`

Statement-1 (Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement- 1 If A, B, C are matrices such that abs(A_(3xx3))=3, abs(B_(3xx3))= -1 and abs(C_(2xx2)) = 2, abs(2 ABC) = - 12. Statement - 2 For matrices A, B, C of the same order abs(ABC) = abs(A) abs(B) abs(C).

Let A, B and C are nxxn matrices such that |A|-2, |B|=3 and |C|=5 . If |(2A)^(2)(3B)(5C)^(-1)|=(1728)/(125) , then the value of n is equal to

Statement 1: if a ,b ,c ,d are real numbers and A=[a b c d]a n dA^3=O ,t h e nA^2=Odot Statement 2: For matrix A=[a b c d] we have A^2=(a+d)A+(a d-b c)I=Odot

If A_(2xx3),B_(4xx3) and C_(2xx4) are three matrices, then which of the following is/are defined?

Let B and C be two square matrices such that BC=CB and C^(2)=0 . If A=B+C then A^(3)-B^(3)-3B^(2)C is

If n(A xx B) = 24, n(B xx C) = 36 , and n(B) = 3 , then n(A xx C) =

Let A be a matrix of order 3xx3 such that |A|=3 . Let B=3A^(-1) and C =(adjA)/(2) , then the value of |A^(2)B^(3)C^(4)| is

If A,B and C are n xx n matrices and det(A)=2,det(B)=3 and det(C)=5 then the value of the det (A^(2)BC^(-1)) is equal to