(a) Factorize the determinant of the following matrix without the use of direct expansion with r = a^6 + 10.
(b) Let A, B, C, and D be the following 4x4 matrices shown below.
It is known that the determinant of A is 3. Find the determinants of the matrices BC and D in terms of A.
(c) (i) Let A be a square matrix such that A^T = -A. Prove that det(A) = 0.
(ii) Let A be a square matrix of odd order for which A^T = -A. Prove that det(A) = 0.
(iii) Let A be a matrix such that A^4 = A^-1. Prove that det(A) = 1.
