Multidimensional matrix inversions (Q1921477)

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 an application of our matrix inversion, we derive new multidimensional bibasic summation formulas.