(a) Show that if c is real number and A = M, (R), then det(CA) =...

  

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(a) Show that if c is real number and A = M, (R), then det(CA) = c" A (b) Show that if A = A, then det(A) = 1 -1 (c) Show that if A = A, then det(A) = 1. 2k+1 (d) Show that if A is nonsingular matrix and k N such that A+1 = A, then det(A) = 1. (e) Show that if det(A) = 0, then det(A. B)=0 (f) Show that if A" =0 for some positive integer n, then det(A)=0 (a) Show that if c is real number and A = M, (R), then det(CA) = c" A (b) Show that if A = A, then det(A) = 1 -1 (c) Show that if A = A, then det(A) = 1. 2k+1 (d) Show that if A is nonsingular matrix and k N such that A+1 = A, then det(A) = 1. (e) Show that if det(A) = 0, then det(A. B)=0 (f) Show that if A" =0 for some positive integer n, then det(A)=0