5. (1 point) K=_ Evaluate the following determinant. 9. (1 point) A square matrix A is skew-symmetric if A = -A. If A is an a X a skew-symmetric matrix where n is odd, prove that dot(A) = 0. Proof: 10. (1 point) Suppose A. B.C.D.E are all square matrices of the same size. Since AT = -A, thus [? But since der (A?) = der (A), thus Show that if ABCDE is invertible, then C is invertible. 2 And since det(-A) = (-1)" del(A), we have ? If a is odd, then 2 det(A) = 0 which gives us that ? Proof: Q.E.D. Since ABCDE is invertible them ? Since det (ABCDE) =[? thus ? Therefore ? Hence C is invert- ible. Q.E.D. A. det (AT) = det(A) B. det(A) = del(-AT) C. det(A) = det(-A) A. det(A) det( B') det(C) det(D) det (E) D. det(A) = 2 B. det(A) det (B) det(C) det(D) det(E) = 0 E. del(A) =0 C. det(ABCDE) # 0 F. det (AT) = det(-A) D. det(A) det ( B) det (C) det(D) det (E) # 0 G. det(A) = (-1)" det(A) E. det (C) # 0 H. det(A) = (-1) det(A) F. det(C) =0 G. del(ABCDE) =0