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If I have block matrices A,B,C and D all of which are non singular would this relationship hold; my main concern is preserving order of matrix multiplication:

if ADB=C

then AD=B^-1C

D=B^-1CA^-1

D^-1 = (BC^-1A)

Also is it okay to assume the inverse of a block matrix is equal to a matrix that contains as its elements the inverse of each individual block?

Thanks for any help

Emma

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# Matrix multiplication preserve order Block matrix

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