Practice problem
Let AAA and BBB be invertible matrices. Which of the following are always true?
(A+B)−1=A−1+B−1(A + B)^{-1} = A^{-1} + B^{-1}(A+B)−1=A−1+B−1
(AT)−1=(A−1)T(A^T)^{-1} = (A^{-1})^T(AT)−1=(A−1)T
(AB)−1=A−1B−1(AB)^{-1} = A^{-1}B^{-1}(AB)−1=A−1B−1
For any constant x≠0x \not= 0x=0, (Ax)−1=A−1x(Ax)^{-1} = A^{-1}x(Ax)−1=A−1x.
(AB)−1=B−1A−1(AB)^{-1} = B^{-1}A^{-1}(AB)−1=B−1A−1
For any constant x≠0x \not= 0x=0, (Ax)−1=A−1x(Ax)^{-1} = \frac{A^{-1}}{x}(Ax)−1=xA−1.
Type a concept, like “slope” or “photosynthesis”.