  The ideal I generated by the 2x2 quantum minors in the algebra A =
O_q(M_{m,n}(k)) (the quantized coordinate algebra of mxn matrices) is
investigated. Analogues of the First and Second Fundamental Theorems of
Invariant Theory are proved. In particular, it is shown that I is a completely
prime ideal, that is, A/I is an integral domain, and that A/I is the ring of
coinvariants of a coaction of k[x,x^{-1}] on O_q(k^m) tensor O_q(k^n), a tensor
product of two quantum affine spaces. (That the ideal of A generated by the txt
quantum minors, for any t, is completely prime is proved in the authors' paper
`Quantum determinantal ideals'.) There is a natural torus action on A/I induced
by an (m+n)-torus action on A. We identify the invariant prime ideals for this
action and deduce consequences for the prime spectrum of A/I.
