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    Bijection between $A \times B$ and $B \times A$

    E-MUN-5-1

    Area
    Topology
    Topics
    Cartesian Products
    Status
    draft

    Show there is a bijective correspondence of \(A \times B\) with \(B \times A\) .

    Solution

    Define \[ \tau:A\times B\longrightarrow B\times A, \qquad \tau(a,b)=(b,a). \] Then \(\tau\) is its own inverse: \[ \tau(\tau(a,b))=(a,b). \] Hence \(\tau\) is bijective.

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