M1 shows the change in A 1 (useful to know) when a matrix is subtracted from A. Check

QUESTION:

M1 shows the change in A 1 (useful to know) when a matrix is subtracted from A. Check part 3 by carefully multiplying MM1 to get I: 1. M = I uvT and M1 = I +uvT/(1v Tu). 2. M = AuvT and M1 = A 1 +A 1uvTA 1/(1v TA 1u). 3. M = I UV and M1 = In +U(Im VU) 1V. 4. M = AUW1V and M1 = A 1 +A 1U(W VA1U) 1VA1 . The four identities come from the 1, 1 block when inverting these matrices: " I u v T 1 # " A u v T 1 # "In U V Im # "A U V W#