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I'm specifically trying to compute (VΔY^{T})^{-1}, where V is nxn and orthogonal, Δ is diagonal, and Y is nonsingular.

In general we have (AB)^{-1}= B^{-1}A^{-1}

But how do we do this in general for many matrices? Is there a method, and as long as the matrix dimensions agreed, does the structure (i.e. orthogonal, nonsingular, SPD, etc) matter when computing the inverse of multiple matrices?

I can't find this anywhere on the internet.

Thanks

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# Several matrix inverse properties

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