Using CASE within UPDATE

[skunkbad]

I'm trying to evaluate field A and update field A and B accordingly. If A = 0, then A should be updated to 1. If A was already 1, then B should be updated to 1. It seems like it should be so simple, but it's not working:

UPDATE `the_table` 
SET `A` = CASE
			WHEN `A` = 0
			THEN `A` = 1
			ELSE `A`
		END,
	`B` = CASE
			WHEN `A` = 1
			THEN `B` = 1
			ELSE `B`
		END
WHERE `ID` = 1

What am I doing wrong?

[skunkbad]

I figured it out:

UPDATE `the_table` 
SET `B` = CASE
			WHEN `A` = 1
			THEN 1
			ELSE `B`
		END,
`A` = CASE
			WHEN `A` = 0
			THEN '1'
			ELSE `A`
		END
WHERE `ID` = 1