(a) The n × n matrices A, B, C, and X satisfy the equation AX(B+ CX) ?1 = C Write an expression for the matrix X in terms of A, B,and C. You may assume invertibility of any matrix whennecessary.
(b) Suppose D is a 3 × 5 matrix, E is a 5 × c matrix, and F is a4 × d matrix. Find the values of c and d for which the statement“det(DEF) = 1” can be valid. Explain your answer.
(c) Find all (real or complex) values of x such that the matrixGH is invertible, where G =
x^2, ?1
x , x ? 2
H = x ? 1 , ?2
1 , x + 1
