In this exercise, we prove the determinantal product formula (1.82). (a) Prove that if E is any

Question:

In this exercise, we prove the determinantal product formula (1.82).
(a) Prove that if E is any elementary matrix (of the appropriate size), then
det(E B) = det E det B.
(b) Use induction to prove that if
A = E1 E2 ∙ ∙ ∙ En
is a product of elementary matrices, then det( AS) = det A det 5. Explain why this proves the product formula whenever A is a nonsingular matrix