Suppose A, B are two 3×3 matrices such that A–1 exists. Then (A−B)A−1(A+B) is equal to
(A+B)A−1(A−B)
A−1B+B2
I−BAB−1(A−B)
I+BAB−1(A+B)
(A−B)A−1(A+B)=I−BA−1(A+B)=A+B−BA−1A−BA−1B=A−BA−1B=A+B−BA−1A−BA−1B=(A+B)−BA−1(A+B)=(A+B)I−BA−1=(A+B)A−1(A−B)