Matrix multiplication preserve order Block matrix

[EmmaSaunders1]

Hello,

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

 

[I like Serena]

Hi EmmaSaunders1!

Your multiplications are a little off.
They should be:

ADB=C
ADBB^-1=CB^-1
AD=CB^-1
D=A^-1CB^-1
D^-1 = (BC^-1A)

You can check the last step by calculating DD^-1.

(Btw, you can use the x² just above the reply box to get nice superscripts. )


And yes, it is 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.
You can check this by creating an example, and see how the matrices multiply.

 

[EmmaSaunders1]

Thats great thanks for that