# Matricies

• Aug 19th 2009, 03:34 AM
manalive04
Matricies
Show that if A and B are two n x n matricies with inverses \$\displaystyle A^{-1}\$ and \$\displaystyle B^{-1}\$, then AB has an inverse and that \$\displaystyle (AB)^{-1} = B^{-1} A^{-1}\$
• Aug 19th 2009, 03:53 AM
mr fantastic
Quote:

Originally Posted by manalive04
Show that if A and B are two n x n matricies with inverses \$\displaystyle A^{-1}\$ and \$\displaystyle B^{-1}\$, then AB has an inverse and that \$\displaystyle (AB)^{-1} = B^{-1} A^{-1}\$

Calculate \$\displaystyle (AB) (B^{-1} A^{-1})\$ and \$\displaystyle (B^{-1} A^{-1}) (AB)\$. What do you find?
• Aug 19th 2009, 04:09 AM
manalive04
matricies
Quote:

Originally Posted by mr fantastic
Calculate \$\displaystyle (AB) (B^{-1} A^{-1})\$ and \$\displaystyle (B^{-1} A^{-1}) (AB)\$. What do you find?

please explain this further i dont understand - sorry
• Aug 19th 2009, 04:25 AM
mr fantastic
Quote:

Originally Posted by manalive04
please explain this further i dont understand - sorry

There's nothing further to explain .... Do the matrix multiplications!