Alan G. answered • 03/18/16
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The answer is that, if A is a square matrix of order n×n, det(cA) = cndet(A).
To prove this, remember that multiplying any row or column of a square matrix by a constant c will change the determinant by a factor of c. (If you do not know this fact, you should read your textbook as it is a standard fact about determinants. I could prove it for you, but you need to do some of the work yourself.)
Multiplying a matrix by a constant c is the same as multiplying every row or column by c, Since A has n rows/columns, you are actually multiplying det(A) by c n-times, which gives the result.
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