There is α'γ=β'γ=0 (note:' stands for transposition).

So Aγ=(αα'+2ββ')γ=0.

So Q=(α, β, γ)

It is known that AQ=A(α, β, γ) = (α, 2β, 0)=Q times diag ().

So q (- 1) AQ = diag ()

So | 2a+3e | =| q (-1) (2a+3e) q | = | 2diag ()+3e |

= | Diag (5,7,3) | = 5 times 7 times 3= 105