谁能帮我解答下面英语线性代数题Let A n*n and Bn*n are such that AB is invert

谁能帮我解答下面英语线性代数题
Let A n*n and Bn*n are such that AB is invertible. Show that both A and B are invertible.
Hint: If A n*n is invertible ,then for any X n
蓝冰出逃 1年前 已收到1个回答 举报
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水鱼灵动 幼苗

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forget the hint.prove:det(AB)=det(A)det(B)≠0,（AB is inversible) so det(A)≠0 and det(B)≠0 that means both A and B are invertible.anothern=rank(AB)≤rank(A)≤n n=rank(AB)≤rank(B)≤n so rank(A)=rank...

1年前

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