Question: Partitioning large square matrices can sometimes make their inverses easier to compute, particularly if the blocks have a nice form. Verify by block multiplication that

Partitioning large square matrices can sometimes make their inverses easier to compute, particularly if the blocks have a nice form. Verify by block multiplication that the inverse of a matrix, if partitioned as shown, is as claimed. (Assume that all inverses exist as needed.)

A B P Q %D

Where P = (A - BD^-1 C)^-1,
Q = -PBD^-1, R = -D^-1CP, and S = D^-1 + D^-1CPBD^-1

A B P Q %D

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