SOLUTION: If A is a square matrix of order 3 and |A| = � 2, find the value of |�3A|. If A = 2B where A and B are square matrices of order 3 � 3 and |B| = 5, what is |A|? If A is a non

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Question 866745: If A is a square matrix of order 3 and |A| = � 2, find the value of |�3A|.
If A = 2B where A and B are square matrices of order 3 � 3 and |B| =
5, what is |A|?
If A is a non-singular matrix of order 3 and |A| = � 3 find |adj A|.
Given a square matrix A of order 3 � 3 such that |A| = 12 find the value
of |A adj A|.
If A is a square matrix of order 3 such that |adj A| = 8 find |A|

Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
1) |-3A| = -3^3 |A| = -27 times -2 = 54
2) A = 2B, |2B| = 2^3 times 5 = 40, then |A| = 40
3) Since A * (adj A) = |A| * I, and A is 3 x 3, we obtain
|A * (adj A)| = |A|^3 = (-3)^3 = -27
-27 = |A * adj A| = |A| |adj A| = -3 |adj A|
therefore |adj A| = 9
4) |A * (adj A)| = |A|^3 = 12^3 = 1728
5) |A * (adj A)| = |A|^3
|A| |adj A| = |A|^3
|adj A| = |A|^2
8 = |A|^2
2.8284271247461900976 = |A|