# Multidimensional matrix inversions and *A*_{r} and *D*_{r}
basic hypergeometric series

### (34 pages)

**Abstract.**
We compute the inverse of a specific infinite *r*-dimensional
matrix, thus unifying multidimensional matrix inversions recently
found by Milne, Lilly, and Bhatnagar. Our inversion is an
*r*-dimensional extension of a matrix inversion previously found
by Krattenthaler. We also compute the inverse of another infinite
*r*-dimensional matrix. As applications of our matrix inversions,
we derive new summation formulas for multidimensional basic
hypergeometric series.

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