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Decide Whether or Not the Matrices Are Inverses of Each

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Decide whether or not the matrices are inverses of each other.
- [5171] and [12127252]\left[ \begin{array} { l l } - 5 & 1 \\- 7 & 1\end{array} \right] \text { and } \left[ \begin{array} { c c } \frac { 1 } { 2 } & - \frac { 1 } { 2 } \\\frac { 7 } { 2 } & - \frac { 5 } { 2 }\end{array} \right]


Definitions:

Filter

A device or process that removes impurities, particulates, or specific elements from a flow of liquid, air, or data, allowing only desired materials or information to pass through.

Negotiate Costlessly

The ability to come to mutual agreement without incurring any transaction costs or facing obstacles in the negotiation process.

Coase Theorem

Principle that when parties can bargain without cost and to their mutual advantage, the resulting outcome will be efficient regardless of how property rights are specified.

Externalities

Costs or benefits that affect parties who did not choose to incur those costs or benefits, often leading to market failures.

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