If L and U are invertible, then $(LU)^{−1}$ = $U^{−1}L^{−1}$. Find $A^{−1}$ from the given LU factorization:
$A = LU = \left[\begin{array}{cc} 1 &5\cr -6 &-36 \end{array}\right]= \left[\begin{array}{cc} 1 &0\cr -6 &1 \end{array}\right]\left[\begin{array}{cc} 1 &5\cr 0 &-6 \end{array}\right]$

$A^{-1} =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$$\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$ $=$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$