1 Show that if A is invertible, then det A det A What theorem(s) should be used to examine the quantity det A'? Select all that apply. A. A square matrix A is invertible if and only if det A +0. B. If one row of a square matrix A is multiplied by k to produce B, then det B = k (det A). . If A is an nxn matrix, then det A' = det A. D. If A and B are nxn matrices, then det AB = (det A)(det B). Consider the quantity (det A) (det A1). To what must this be equal? O A. det A B. det I O C. det A? O D. det A-1 To what scalar must this new determinant be equal? (Simplify your answer.) 1 ? det A Therefore, why is det A1 Therefore, why is det A :? det A 1 O A. Since (det A) (det A') = 0, it follows from algebra that det A det A B. Since (det A) (det A-1) = det (A"), det A must be equal to det (A') OC. Since (det A) (det A1) = det A, the previous theorem states that det A = det A. 1 D. Since (det A)(det A) = 1, it follows from algebra that det A det A