Remove-mailboxDatabase

get-mailbox | remove-mailbox

To remove the administrator mailbox

get-mailbox -id administrator | disable-mailbox

To remove the arbitrary mailbox

get-mailbox -Database "Mailbox Database 1575725052" -Arbitration | Remove-Mailbox -Arbitration

Exchange can't remove the arbitration mailbox "vanarts.com/Users/SystemMailbox{1f05a927-bff0-4492-acc5-
4b1191342fb2}" because it's the last one in the organization. + CategoryInfo : InvalidOperation: (vanarts.com/Use...5-4b1191342fb2}:ADObjectId) [Remove-Mailbox],
InvalidOperationException + FullyQualifiedErrorId : 78359DD3,Microsoft.Exchange.Management.RecipientTasks.RemoveMailbox

Confirm
Are you sure you want to perform this action?
Removing the Mailbox "vanarts.com/Users/SystemMailbox{e0dc1c29-89c3-4034-b678-e6c29d823ed9}" will remove the Active
Directory user object and mark the mailbox in the database for removal.
[Y] Yes [A] Yes to All [N] No [L] No to All [?] Help (default is "Y"):
Confirm
Are you sure you want to perform this action?
Removing the Mailbox "vanarts.com/Users/FederatedEmail.4c1f4d8b-8179-4148-93bf-00a95fa1e042" will remove the Active
Directory user object and mark the mailbox in the database for removal.

To remove the last arbitrary mailbox

get-mailbox -Database "Mailbox Database 1575725052" -Arbitration | Disable-Mailbox -Arbitrary -DisableLastArbitrationMailboxAllowed

Confirm
Are you sure you want to perform this action?
Disabling Mailbox "vanarts.com/Users/SystemMailbox{1f05a927-bff0-4492-acc5-4b1191342fb2}" will remove the Exchange
properties from the Windows user object and mark the mailbox in the database for removal.
[Y] Yes [A] Yes to All [N] No [L] No to All [?] Help (default is "Y"):

If you use Remove-Mailbox -Arbitration -RemoveLastArbitrationmailboxAllowed, the following error will pop up.

The arbitration mailbox "adatum.com/Users/SystemMailbox{e0dc1c29-89c3-4034-b678-e6c29d823ed9}" is used by Exchange and can't be removed. + CategoryInfo : NotSpecified: (adatum.com/User...8-e6c29d823ed9}:ADObjectId) [Remove-Mailbox], Recipient TaskException + FullyQualifiedErrorId : 5E8509C3,Microsoft.Exchange.Management.RecipientTasks.RemoveMailbox The arbitration mailbox "adatum.com/Users/FederatedEmail.4c1f4d8b-8179-4148-93bf-00a95fa1e042" is used by Exchange and can't be removed. + CategoryInfo : NotSpecified: (adatum.com/User...bf-00a95fa1e042:ADObjectId) [Remove-Mailbox], Recipient TaskException + FullyQualifiedErrorId : 56206E20,Microsoft.Exchange.Management.RecipientTasks.RemoveMailbox

Solution:

Disable-Mailbox -Arbitration "System*" -DisableLastArbitrationMailboxAllowed

Disable-Mailbox -Arbitration "Fede*" -DisableLastArbitrationMailboxAllowed