Question: (a) (Computing the inverse of a block matrix. ) Let A = ( A, Am (All A12 Assume that An and Azz are square and

(a) (Computing the inverse of a block matrix. ) Let A = ( A, Am (All A12 Assume that An and Azz are square and that An and Azz - AziAn Alz are nonsingular. Let B = An Biz ) be the inverse of A. Then show that B2? = (A12 -- A21AT A12)", B12 = - AT Al Biz, B31 = - B22 A 21 AT n, and Bul = AP - B12AZI An

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