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.)

-1 B [c D.

-(BD¯'C)-! D'C(BD-'C)-! D' – D-C(BD¯'C)-'BD

-1 B [c D. -(BD'C)-! D'C(BD-'C)-! D' D-C(BD'C)-'BD" ! (BD'C)-'BD'

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