Re: [代數] subgroup
※ 引述《s620555 (小毛)》之銘言：
: 麻煩幫解
: 1) show that {A屬於GLn(R)∣det A = ±1 } is a subgroup of GLn(R) un-der
: multiplication
有人解了 不過還是提供另外一個方法
Consider f: GLn(R) -> R\{0}, f=(det)^2.
(R\{0} is a group under the natural multiplication)
f(AB) = (det(AB)^2) = (detA)^2 (detB)^2 = f(A)f(B).
Hence, f is a homomorphism.
The set {A is in GLn(R) | det A = 1 or -1} = ker f is a subgroup of GLn(R).
僅供參考 有錯請指正~~~~
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