# Several matrix inverse properties

1. Nov 1, 2012

### pob1212

Hi,

I'm specifically trying to compute (VΔYT)-1, where V is nxn and orthogonal, Δ is diagonal, and Y is nonsingular.

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

2. Nov 1, 2012

### micromass

$$(ABC)^{-1}=(A(BC))^{-1}=(BC)^{-1}A^{-1}=C^{-1}B^{-1}A^{-1}$$

Was that what you were looking for?

3. Nov 1, 2012

### pob1212

exactly what I was looking for. Thanks