Let A, B, C, D, and I be n x n matrices. Use the definition or properties of a determinant to justify the following formulas. Part (c) is useful in applications of eigenvalues (Chapter 5). a. det = det A b. det = det D D D| = (det A)(det D) B c. det det D

Q: c.) (CD) (CD) -1 = d.) cofactor of B =

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Q: Q4: Using Cayley - Hamilton theorem to find the inverse of the matrix A, where 1 1 2 A = 3 1 1 2 3 1

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Q: 100 110 0 121 :/つ

A: Please see the below pictures for detailed solution.

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Q: 1 if k = i and l = j if k = j and l = i if k = l but k # i, j 1 (Si3)ke = 1 otherwise.

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Q: e) Show that the determinant of the nxn matrix 320 132 DOO 00 . . 000 0 0 0 15 equals to 2+₁ n+1 132…

A: Given Matrix: 320..000132..000........................000..132000..013 and of order n×n.   To prove:…