Help on a matrix problem.

'The Matrix

A = ( -1 1 -1)

( 0 c 0)

(3+2c-c^2 b 3)

can only be diagonalised for some values of the parameters b and c . Construct a table

showing the values of b and c for which diagonalisation is possible. You must show

your working.'

For this I have done the following:

eigenvectors -1

P(ƛ) = -(c -ƛ)((-1-ƛ)(3-ƛ)+3+2c-c^2)

For what I finally got

c-ƛ =0 -> ƛ =c

Then ƛ^2 -2ƛ +2C -ƛ^2=0

and then getting the value for ƛ

ƛ = 1+-(1-c)

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Is this right?

And what should I do next with this problem?

Thank you for your time.