Prove that if M is a n x n matrix that can be written in

where A and C are square matrices, then det(M) = det(A) det(C)

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- Mar 18th 2008, 11:08 AMtttcomraderSquare matrices within a matrix
Prove that if M is a n x n matrix that can be written in

where A and C are square matrices, then det(M) = det(A) det(C) - Mar 18th 2008, 11:23 AMiknowone
Write the matrix in Jordan normal form with on the diagonal and 0's below the diagonal. Then Likewise matrix can be written in this form and we know .

But then the entire matrix is in Jordan normal form with on the diagonal and 0's below the diagonal, thus .