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Problem 2 - Entrance Test

If A is a square matrix of order 3 and |adj A| = 64, then |A| =

Correct: A

We know that |adj A| = |A|^(n-1), where n is the order of the matrix A. Here, n=3 and |adj A| = 64. So, 64 = |A|^(3-1) = |A|^2. Therefore, |A| = √64 = 8.