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Question:

If A is a 3x3 matrix |3A| = k|A|, then write the value of k.

Solution:

If A is an nxn matrix then for any integer p, |pA| = pn|A|
Since here A is 3x3 matrix , we get |3A| = 33|A| which is equal to k|A| (given).
Therefore k = 33 = 27.