# Find values of “a” so “A” eigenvalues absolute values are 1 or less. Applicable theorem?

I´m taking linear algebra, and the professor asked us to get back next class with many methods to solve this exercise. I can´t find even one after 2 hours of thinking, really sad. Could you please help?

I´ve the following matrix "A", which represent a linear transformation:

 a   0  -2a 0
2a -3a  0 -2a
-a   0   3a 0
0   a  -a  2a


and I need to find what the title says.

Notice that we can write the matrix as $aM$ for some other matrix $M$. Then use the defining equation of an eigenvalue or your favorite computational methods to determine how to compute the eigenvalues of $M$, and apply your restriction.