EXERCISE 4.4.2: Proving that the determinant of a matrix and the transpose of the matrix are equal. Prove. (a) If A is an n x n matrix then det A = det AT

Find the determinant of the matrix in Exercise 16 using the method of expansion by cofactors. Use a the third row and b the first column. 16. [342631478]

Find the determinant of the matrix in Exercise 15 using the method of expansion by cofactors. Use a the second row and b the second column. 15. [321456231]

Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.