1.Use mathematical induction to prove that if A is an (n+1) ×(n+1) matrix
with two identical rows then det(A) = 0
2.Let A and B be 2 ×2 matrices.
(a)Does det(A+B) = det(A) + det(B)？
(b)Does det(AB) = det(A)det(B)？
(c)Does det(AB) = det(BA)？
Justify answers.
3.Let A and B be 2 ×2 matrices and let
┌ ┐ ┌ ┐ ┌ ┐
│a11 a12│ │b11 b12│ │0 α│
C = │ │ D = │ │ E = │ │
│b21 b22│ │a21 a22│ │β 0│
└ ┘ └ ┘ └ ┘
(a)Show that det(A+B) = det(A) + det(B) + det(C) + det(D)
(b)Show that if B = EA then det(A+B) = det(A) + det(B)
以上，麻煩好心的大大！（鞠躬
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