Let A be a `nxxn` matrix such that`A ^(n) = alpha A,` where `alpha ` is a
real number different from 1 and - 1. The matrix `A + I_(n)` is

Let A be an nxxn matrix such that A+A^(')=O_(nxxn) then |I+lamdaA^(2)|geM where 3M+1 is __

Let A be an nxxn matrix such that A+A^(')=O_(nxxn) then |I+lamdaA^(2)|geM where 3M+1 is __

The number of nxxn matrix A and B such that AB - BA = I is. . .

(aA)^(-1)=(1)/(a)A^(-1) , where a is any real number and A is a square matrix.

Rank of the following (n+1)xx(n+1) matrix,where a is a real number,is

Matrix A is such that A^(2)=2A-I , where I is the identify matrix. Then for n ne 2, A^(n)=

Let A be a non - singular square matrix such that A^(2)=A satisfying (I-0.8A)^(-1)=I-alphaA where I is a unit matrix of the same order as that of A, then the value of -4alpha is equal to

Let A be a non - singular square matrix such that A^(2)=A satisfying (I-0.8A)^(-1)=I-alphaA where I is a unit matrix of the same order as that of A, then the value of -4alpha is equal to

Matrix A such that A^(2)=2A-I , where I is the identity matrix, then for n ge 2, A^(n) is equal to

Matrix A such that A^(2)=2A-I , where I is the identity matrix, then for n ge 2, A^(n) is equal to