Let P be a 3 × 3 matrix such that `P^T=lambdaP+muI,lambda, mu in R` , where `lambda ne pm 1, mu ne 0` and `P^T` denotes transpose of matrix P then :

If A=[[cos alpha, -sin alpha],[ sin alpha, cos alpha]] , then the number of values of alpha in (0, pi) satisfying A+A^T=I_, is [Note: I is an identity matrix of order 2 and P^T denotes transpose of matrix P .]

If P is a 3xx3 matrix such that P^T = 2P+I , where P^T is the transpose of P and I is the 3xx3 identity matrix, then there exists a column matrix, X = [[x],[y],[z]]!=[[0],[0],[0]] such that

If P is a 3xx3 matrix such that P^T = 2P+I , where P^T is the transpose of P and I is the 3xx3 identity matrix, then there exists a column matrix, X = [[x],[y],[z]]!=[[0],[0],[0]] such that

If P is a 3xx3 matrix such that P^T = 2P+I , where P^T is the transpose of P and I is the 3xx3 identity matrix, then there exists a column matrix, X = [[x],[y],[z]]!=[[0],[0],[0]] such that

If P is a 3xx3 matrix such that P^(T) = 2P +I, where P^(T) is the transpose f P and I is the 3xx3 identify matrix then there exists a column matrix X = [(x),(y),(z)] != [ (0),(0),(0)] such that :

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

If P is a 3xx3 matrix such that P^(T)=2P+I where P^(T) is the transpose of P and I is the 3xx3 identity matrix,then there exists a column matrix,X=[[xyz]]!=[[000]] such that

If A=[[4,1],[5,8]] , show that A+A^T is symmetric matrix, where A^T denotes the transpose of matrix A