If A is a square matrix such that `A^2 = A and (I + A)^n = 1 +lambda A,` then `lambda=`

Which of the following is/are correct ? (i) Adjoint of a symmetric matrix is also a symmetric matrix. (ii) Adjoint of a diagonal matrix is also a diagonal matrix. (iii) If A is a square matrix of order n and lambda is a scalar, then adj ( lambda A)= lambda^(n) adj(A) (iv) A (adj A) = (adj A) A = |A| I

If A is a square matrix of order nxxn such that |A|=lambda , then write the value of |-A| .

If A is a square matrix of order nxxn such that |A|=lambda , then write the value of |-A| .

If A is a square matrix of order n, then det |lambdaA | is equal to (lambda being a scalar)

If X is a non-zero column matrix, such that A X=lambda X where lambda is a scalar and the matrix A is [[4,6,6],[1,3,2],[-1,-5,-2]] then sum of distinct values of lambda is

If A and B are square matrices of order n, then A - lambda I and B - lambda I commute for every scalar lambda only if a)AB = BA b) AB + BA = 0 c)A = - B d)None of these

" If "A" is a square matrix of order "n" ,then "|adj[lambda A)|" is equal to "