I\'ve checked the answer in Linear Algebra and ItsApplications and compared to t

Question

I've checked the answer in Linear Algebra and ItsApplications and compared to the solutions here on Cramster.They differed on b, c and i. My answer was identical to the onehere on Cramster, so I'm suspecting a printing error in the book.
Anyway, here are the relevant parts of the exercise:
Mark each statement True or False. Justify each answer. Assumethat all matrices here are square.
b) If two rows of a 3 x 3 matrix A are the same, then det(A) =0. c) If A is a 3 x 3 matrix, then det(5A)=5det(A). i) det(AT) = -det(A)
Anyway, here are the relevant parts of the exercise:
Mark each statement True or False. Justify each answer. Assumethat all matrices here are square.
b) If two rows of a 3 x 3 matrix A are the same, then det(A) =0. c) If A is a 3 x 3 matrix, then det(5A)=5det(A). i) det(AT) = -det(A)

Explanation / Answer

b ) two rows of 3x3 matrix are identical. i.e. one row is a scalar multiple of the other. so, they are dependent. so, by applying elementary operations , one row will becomezero. so, the determinant is zero. (c) multiplying a matrix of order n with a scalark is nothing but multiplying any row with k. where as , multiplhing any one row or colunn will haveno impact on the determinant   the matrix.

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