Let A = [a b c, d e f, g h i]. B = [9 3h i, 2d 6e 2f, a 3b c]. Suppose that det (A) = 2. Find (det (AB)^T). Answer is 24. How do I find the answer with the right steps?
3 answers
Answer is -24.
If all the elements of a row or column of A are multiplied by k, then |A| → k|A|
Since The middle row of B is that of A multiplied by 2 and the middle column of B is multiplied by 3.
So, |B| = 2*3*|A|
That means |AB| = |A|*|B| = 2*12
and then |AB|T = -|AB|
Since The middle row of B is that of A multiplied by 2 and the middle column of B is multiplied by 3.
So, |B| = 2*3*|A|
That means |AB| = |A|*|B| = 2*12
and then |AB|T = -|AB|
Thank you!