Theory of Computation

The concatenation of strings x and y is the string xy. For example, the concatenation of the strings 1001 and 110 is the string 1001110. The concatenation operation for languages is defined as follows. Let A and B be languages. The concatenation of A and B is the language, denoted A fit B, consisting of all possible strings xy where x subset A and y subset B. Prove that if both A and B are in PSPACE, then A fit B is also in PSPACE