The number of values of λ for which there exist a non-zero 3x3 matrix A such that A′=λA is :

We haveA=A′′=(λA)′=λA′=λ2A.As A≠0,λ2=1⇒λ=±1.For λ=1 all non-zero symmetric matrices can work as A.For λ=-1, all non-zero skew symmetric matrices can work as A.