Question: 1. Let A. B. C, D be real n x n matrices. The block matrix A B D has size (2n) x (2n). a). Show

1. Let A. B. C, D be real n x n matrices. The block matrix A B D has size (2n) x (2n). a). Show that det A B 0 D = det A det D. b). Prove let -13 3 20. Hint. Use line or column operations involving the complex number i. c). Assume A is invertible. Prove the identity det C B D = det(AD - ACA ' B). Hint. Factor to the left the matrix A and then use row / column operations as in the case of scalar matrices. d) Let X be another n x n matrix. Prove det XA XB = det X det B D e). Show the identity

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