Suppose $A$ and $B$ are $n \times n$, B is invertible, and AB is invertible

Suppose $A$ and $B$ are $n \times n$, B is invertible, and AB is invertible


J
Asked by 3 years ago
240 points

Suppose $A$ and $B$ are $n \times n$, B is invertible, and AB is invertible. Show that $A$ is invertible [Hint: Let $C=AB$, and solve this equation for $A$

Suppose $A
jeffp

2 Answers

Answered by 3 years ago
8.7k points

start with the hint,

$$C=AB \longrightarrow CB^{-1}=ABB^{-1} \longrightarrow A=CB^{-1}$$

since C and B are both invertible and the product of two invertible matrices is invertible then $A$ must be invertible.

Z
Answered by 2 years ago
0 points

Oh Snap! This Answer is Locked

Suppose $A$ and $B$ are $n \times n$, B is invertible, and AB is invertible

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Asked: 3 years ago

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