Show that if A is invertible, then det Upper A Superscript negative 1det A−1equals=StartFraction 1 Over det Upper A EndFraction
1 det A. What theorem(s) should be used to examine the quantity det Upper A Superscript negative 1det A−1? Select all that apply. A. If A and B are ntimes×n matrices, then det ABequals=(det Upper A )(det A)(det Upper B )(det B). Your answer is correct.B. If one row of a square matrix A is multiplied by k to produce B, then det Upper Bdet Bequals=ktimes•(det Upper A )(det A). C. A square matrix A is invertible if and only if det Upper Adet Anot equals≠0. Your answer is correct.D. If A is an ntimes×n matrix, then det Upper A Superscript Upper Tdet ATequals=det Upper Adet A. Consider the quantity (det Upper A )(det Upper A Superscript negative 1 Baseline )(det A)det A−1. To what must this be equal? A. det Upper I
