Thread: 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 $\displaystyle (AB)^{-1} = B^{-1} A^{-1}$

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?

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

Originally Posted by manalive04

please explain this further i dont understand - sorry

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