Hi! The base form of the verb is 이다 which means "To be". In present informal polite style: 이다 is transformed into 이에요 when it's followed after final consonant and 예요 when it's followed after final vowel. in past formal plain style: 이다 is transformed into 이었다 when it's followed after final consonant and 였다 when it's followed after final vowel. Examples: 나는 학생 이었다. 나는 바보 였다. Hope this can help you!

yes it is true. 이었다 is the same as 였다, like their pronunciation