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

Answered by Aaron 3 years ago

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.

**Excerpt from file: **LEG 500 Discussion Questions Drawing on arguments found in the reading for this week, determine the appropriate balance between unfettered free speech and the duties of public employees. Provide specific examples to support your response. This weeks readings discussed aspects of freedom of speech

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Surround your text in `*italics*`

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, to write a math equation use, for example, `$x^2+2x+1=0$`

or `$$\beta^2-1=0$$`

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