Hello! I was trying to show that the wedge product of 2 one-forms is a 2-form. So we have ## (A \wedge B)_{\mu \nu} = A_\mu B_\nu - A_\nu B_\mu ##. So to show that this is a (0,2) tensor, we need to show that ##(A \wedge B)_{\mu' \nu'} = \Lambda_{\mu'}^\mu \Lambda_{\nu'}^\nu (A \wedge B)_{\mu \nu}##. But ##A_{\mu'} B_{\nu'} - A_{\nu'} B_{\mu'} = \Lambda_{\mu'}^\mu A_\mu \Lambda_{\nu'}^\nu B_\nu - \Lambda_{\nu'}^\nu A_\nu \Lambda_{\mu'}^\mu B_\mu ##. I am not sure how to proceed from here, as the matrices don't commute, so I can't bring the ##\Lambda## in the front. What should I do?(adsbygoogle = window.adsbygoogle || []).push({});

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# I Wedge Product

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