In a mudarabah-based business, does the rab-al-mal have the right to know which businesses the mudarib chooses to invest the capital in? If, for example, the mudarabah contract clearly requires the mudarib to invest the money only in certain (halal) businesses, but after receiving and working with the capital he refuses to reveal to the rab-al-mal what it is actually invested in or where the profit (if any) is actually coming from, what is the ruling on it?
According to the Bank Negara Malaysia, the rabb-al-mal has "a right of access to reasonable information regarding the mudarabah venture." [Shariah Standard on Mudarabah § 10.5]. While this is classified as a Shariah standard, it does not go into detail on how this ruling is derived or what exactly constitutes "reasonable information."
I have however read from various other sources that a non-transparent mudarabah contract would be, if not verboten, at least strongly discouraged due to the uncertain nature of the contract; there is no shortage of evidence in the hadith literature forbidding gharar (e.g. uncertain sales such as buying fruit before it's ripe or buying fish while it's still in the water), where the buyer have no knowledge of what they're purchasing until after the transaction is complete.
In the case of the rabb-al-mal, he does have the right to know what he's "buying" (read: investing in), and has full authority to establish exactly what the mudarib can or cannot invest in when establishing the mudarabah contract. And if it's proven that the mudarib invested the capital in a way not authorized by the rabb-al-mal, he is very much in breach of contract. I know of no difference of opinion regarding these two points.
Going back to the BNM standard above, it seems likely that "reasonable information" would be what is needed to prevent uncertainty on the part of the rabb-al-mal, which is to say enough to confirm that the mudarib is working according to the contract and to ensure that the profit is being distributed appropriately.
I do not know how universally accepted this ruling would be though; all sources I've examined are from the Malaysian model of Islamic finance, which has been known to differ with Islamic financial models elsewhere (e.g. in the Arab world).
As an aside, I know of no reason you can't just demand transparency as part of the mudarabah contract itself. The mudarib would then be explicitly required to provide such information as part of his contractual (rather than Shariah) obligations.