If `A=[(1,0,0),(0,1,1),(0,-2,4)] , 6A^(-1)=A^2+cA+dI`, then (c,d) is :

Let A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] and A^-1=[1/6(A^2+cA+dI)] Then value of c and d are (a) (-6,-11) (b) (6,11) (c) (-6,11) (d) (6,-11)

Consider a matrix A=[(0,1,2),(0,-3,0),(1,1,1)]. If 6A^(-1)=aA^(2)+bA+cI , where a, b, c in and I is an identity matrix, then a+2b+3c is equal to

If A = [(1 ,0, 0),(0, 1,0),( a,b, -1)] , then A^2 is equal to (a) a null matrix (b) a unit matrix (c) A (d) A

A= [{:( 1,0,0) ,( 0,1,1) , ( 0,-2,4) :}] ,I= [{:( 1,0,0) ,( 0,1,0),( 0,0,1) :}]and A^(-1) =[(1)/(6) (A^(2)+cA +dt)] then , the value of c and d are

If A=[(1,0,0),(0,1,0),(1,b,0] then A^2 is equal is (A) unit matrix (B) null matrix (C) A (D) -A

If A= [(1,0,1), (0,0,1),(a,b,2)] , then a I+b A+2A^2 equals (a) A (b) - A (c) a b\ A (d) none of these

If A=[(2,0,0),(0,cos,sinx),(0,-sinx,cosx)] then (AdjA)^-1= (A) 1/2A (B) A (C) 2A (D) 4A

If A=[(0,0,0,0),(0,0,0,0),(1,0,0,0),(0,1,0,0)] then (A) A^2=I (B) A^2=0 (C) A^3=0 (D) none of these

If A is a square matrix of any order then |A-x|=0 is called the chracteristic equation of matrix A and every square matrix satisfies its chatacteristic equation. For example if A=[(1,2),(1,5)], Then [(A-xI)], = [(1,2),(1,5)]-[(x,0),(0,x)]=[(1-x,2),(1-0,5-x)]=[(1-x,2),(1,5-x)] Characteristic equation of matrix A is |(1-x,2),(1,5-x)|=0 or (1-x)(5-x)(0-2)=0 or x^2-6x+3=0 Matrix A will satisfy this equation ie. A^2-6A+3I=0 . A^-1 can be determined by multiplying both sides of this equation. Let A=[(1,0,0),(0,1,1),(1,-2,4)] On the basis for above information answer the following questions:Sum of elements of A^-1 is (A) 2 (B) -2 (C) 6 (D) none of these

if A =[{:(1,0,2),(0,2,1),(2,0,3):}] , prove that A^3-6A^2+7A+2I=0