Let A, B be nxn matrices. (i) det(2.A) = 2det( A) (ii) det( A + B) = det( A) + det(B) (iii) det( AB) = det( A) det(B) (iv) det(A' ) = det( A) (V) det( AA' ) =1 (vi) det( AB) = det(BAT ) (vii) det( AB-1) _ det( A) det(B) (viii) If row 1 and row 2 of the matrix A are switched, determinant stays the same. (ix) If one of the rows of A is multiplied by 5, the determinant is also multiplied by 5. (x) If one of the rows of A is added to another row of A, the determinant stays the same. Note: Please review the equivalent statements that will mean "the matrix is invertible". (The determinant is not zero, Zero is not an eigenvalue, etc...) True or False?: If A is not invertible, then (i) 0 is an eigenvalue for A. (ii) det( A) = 0 (iii) det( A- I) =0 (I is the identity matrix of the same size)