Let `P` be an `m xx m` matrix such that `P^2 = P`. Then `(1+P)^n` equals

Let P be a non - singular matrix such that I+P+P^(2)+…….P^(n)=O (where O denotes the null matrix), then P^(-1) is

P is a 2xx2 matrix . P'=P^(-1) then P=……..

Let P be a non-zero polynomial such that P(1+x)=P(1-x) for all real x, and P(1)=0. Let m be the largest integer such that (x-1)^m divides P(x) for all such P(x). Then m equals

Let P be a nonsingular matrix, and 1+ P + P^(2) + …….. + P^(n) = O , then find P^(-1) .

Let p be a non singular matrix, and I + P + p^2 + ... + p^n = 0, then find p^-1 .

Let p be a non singular matrix, and I + P + p^2 + ... + p^n = 0, then find p^-1 .

Let p be a non singular matrix, and I + P + p^2 + ... + p^n = 0, then find p^-1 .

Let M and N be two 3xx3 non singular skew-symmetric matrices such that M N=N M . If P^T denote the transpose of P , then M^2N^2(M^T N)^(-1) (M N^(-1))^T is equal to