mat-button-toggle set as checked code example
Example: mat-button-toggle selected default
<mat-button-toggle-group class="right-aligned" value="book">
<mat-button-toggle value="italic" value="edit"><mat-icon>edit</mat-icon></mat-button-toggle>
<mat-button-toggle value="bold" value="book"><mat-icon>import_contacts</mat-icon></mat-button-toggle>
</mat-button-toggle-group>