Do you know what the matter was?

They mean something different.
"What was the matter?" is something close to an idiomatic expression. It's asking about something that was wrong, alop, amiss, that caused problems, and the questioner wants to know what it was. It presupposes that something bad has happened.

But in the case of something like "the matter at hand", you're just talking about the point or the subject that was under discussion or observation. It's value-neutral. "Do you know what the matter was" is more likely to be referring to this sense of "the matter". I suppose it COULD refer to the sense of something bad, but I don't think I'd use it that way.

The first is not wrong.

And disagreeing with MJ, they both mean the same to me.

The second sounds more idiomatic (although it is grammatically more awkward) because it more closely resembles the common usage "what's the matter?"
You could use either, depending on the word you want to stress, which would be the word at the end.

O dear, what can the matter be?
Dear, dear, what can the matter be?
O dear, what can the matter be?
Johnny's so long at the fair.

He promised he'd buy me a fairing should please me,
And then for a kiss, oh! he vowed he would tease me,
He promised he'd bring me a bunch of blue ribbons,
To tie up my bonny brown hair.

Oh, dear, what can the matter be
Three old ladies locked in the lavatory
They've been there from Monday till Saturday
Nobody knew they were there

I completely agree, McTag.



Of course, they could have different meanings depending on whether there was two different situations but, MJ's analysis is nonsense. [unless, of course, he has some other considerations in mind]

CONTEXT CONTEXT CONTEXT



I disagree. The normal neutral situation for these "double question" forms is to only use one question form.

Do you know what the matter was?

That comes in the "Do you know" portion where we have 'do' signaling a question. Since we have the question marked with 'do', there's normally no need for subject verb inversion, "... was the matter", or for another auxiliary question marker [eg. did, do, have, etc.

?? Do you know where did he live? --> Do you know where he lived?

?? Do you understand what does 'preview' mean? --> Do you understand what 'preview' means?

?? Do you realize what has he done? --> Do you realize what he has done?

Having said that, there are times when speakers will use the second form with double question marking.

Do you know what was the matter?

In situations like this, there is often a pause, something like this.

Do you know, what was the matter?

I think it would be relatively rare to see this double question marker form in writing.