According to a grammar book called Grammar in Use
Before a noun we include to be when the nouns tells us what the
subject is, but often leave it out when we give our opinion…We leave
out to be in formal English.
For example :
He walked into what seemed to be cave. ( not … what seemed a cave.)
She seems (to be) a very efficient salesperson.
The job turned out (to be) far easier.
And apparently we cannot omit to be if linking verb is followed by a verb as follows :
The television seems to be working okay now.
I couldn’t find many references regarding this question on the internet so I’d like to ask that do we have to omit to be especially in formal writing even if it is followed by a noun phrase? or is it a strict rule always true?
And can we omit to be before a verb or noun phrase in casual writing as follows ? How do they sound?
The television seems working okay now.
He walked into what seemed cave.
It isn’t a strict rule. I generally use ‘to be’ in both formal and informal contexts.
In your second example, you can’t omit the verb in the first case, it needs to say
The television seems to be working okay now
For the second I think you could say either
He walked into what seemed a cave
He walked into what seemed to be a cave
Source : Link , Question Author : Mrt , Answer Author : rhm