For what is described above, the solution is quite simple, just drop the mat-list-icon into your selector and Material will do the magic:
<mat-list> <mat-list-item *ngFor="let position of cart"> <h3 mat-line> {{ position.name }} </h3> <p mat-line> <span> Line 1 </span> </p> <div> $2.00 </div> <button mat-icon-button (click)="remove(1)"> <mat-icon class="mat-24">delete</mat-icon> </button> </mat-list-item> </mat-list>

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