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: 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 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 two non-singular matrices such that A B=C ,t h e n|B| is equal to (|C|)/(|A|) b. (|A|)/(|C|) c. |C| d. none of these

If a, b, c are the sides of a scalene triangle such that |[a , a^2 , a^(3)-1 ],[b , b^2 , b^(3)-1],[ c, c^2 , c^(3)-1]|=0 , then the geometric mean of a, b c is

Statement 1 : Points A(1,0),B(2,3),C(5,3),a n dD(6,0) are concyclic. Statement 2 : Points A , B , C ,a n dD form an isosceles trapezium or A Ba n dC D meet at Edot Then E A. E B=E C.E D dot

If A=[-1 1 0-2] , then prove that A^2+3A+2I=Odot Hence, find Ba n dC matrices of order 2 with integer elements, if A=B^3+C^3dot

Let a , b , c , d be positive integers such that (log)_a b=3/2a n d(log)_c d=5/4dot If (a-c)=9, then find the value of (b-d)dot

A, B and C are three square matrices of order 3 such that A= diag. (x, y, x), det. (B)=4 and det. (C)=2 , where x, y, z in I^(+) . If det. (adj. (adj. (ABC))) =2^(16)xx3^(8)xx7^(4) , then the number of distinct possible matrices A is ________ .

If sides of triangle A B C are a , ba n dc such that 2b=a+c then b/c >2/3 (b) b/c >1/3 b/c<2 (d) b/c<3/2

Let A=[[1, 2], [3 , 4]] and B = [[a, b],[ c, d]] be two matrices such that they are commutative and c ne 3 b then the value of |(a-d)/(2 b-c)| is