If the rank of the matrix `[(lambda,-1,0),(0, lambda,-1),(-1,0,lambda)]` is 2, then find `lambda`.

If A = [(lambda,1),(-1,-lambda)] , then for what value of lambda,A^(2)=0 ?

If lambda = -2, determine the value of |(0,2lambda,1),(lambda^(2),0,3lambda^(2)+1),(-1,6lambda-1,0)| .

If A = [{:(lambda,1),(-1,-lambda):}] , then for what values of lambda, A^(2) =0 ? …………..

Show that if lambda_(1), lambda_(2), ...., lamnda_(n) are n eigenvalues of a square matrix a of order n, then the eigenvalues of the matric A^(2) are lambda_(1)^(2), lambda_(2)^(2),..., lambda_(n)^(2) .

If lambda = - 2 , determine the value of |{:(0,2lambda,1),(lambda^(2),0,3lambda^(2)+1),(-1,6lambda-1 ,0):}|

If roots alpha, beta of the equation (x^(2)-bx)/(ax-c)=(lambda-1)/(lambda+1) are such that alpha+ beta=0 , then the value of lambda is

Find the value of lambda so that the points P ,Q ,R and S on the sides O A ,O B ,OC and A B , respectively, of a regular tetrahedron O A B C are coplanar. It is given that (O P)/(O A)=1/3,(O Q)/(O B)=1/2,(O R)/(O C)=1/3 and (O S)/(A B)=lambdadot (A) lambda=1/2 (B) lambda=-1 (C) lambda=0 (D) for no value of lambda

If |(a^2+lambda^2, a b+clambda, ca-blambda), (a b-clambda, b^2+lambda^2, b c+a), (ca+blambda, bc-alambda, c^2+lambda^2)| |(lambda, c, -b), (-c,lambda, a), (b,-a,lambda)|=(1+a^2+b^2+c^2)^3 , then he value of lambda is a. 8 b. 27 c. 1 d. -1