no matter (what, who, etc.); even if
Follows a noun or a question word (e.g., 何, 誰, どこ) to mean 'no matter what/who/where' or 'even if'. Often used in formal or written contexts.
No matter what the reason is, being late is being late.
No matter who it is, they cannot enter this room.
Used in the pattern ...であれ...であれ to list alternatives, meaning 'whether ... or ...'. Formal and often written.
Imperative form of である, meaning 'be'. Rare and literary; not used in modern conversational Japanese.
See also: である
Whether it rains or snows, the game will be held as scheduled.
"Be strong," he said.
でも is a more casual and common way to express 'even if' or 'no matter', while であれ is formal and often written.
Derived from the imperative form of the copula である, which itself comes from で (particle) + ある (to be). The concessive use ('no matter') developed from the imperative sense.