Question

A real $4\times 4$ matrix A satisfies the equation $A^2=I$, where I is the $4\times 4$ identity matrix. The positive eigen value of A is.

Answer 1

$A^2=I$ ...(1)
We know that $A{A}^{-1}=I$ ...(2)
From (1) and (2)
$A=A^{-1}$
If $\lambda$ is an eigen value of matrix A then
$\lambda =\frac{1}{\lambda }$
${\lambda }^2=1$
$\lambda =\pm 1$
$\therefore$ Positive eigen value of A =1.