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Let |A| = 6, where A is a 3 3 matrix. If |adj (3 adj (A2 adj(2A) ) ) | = 2m 3n, m, n N, then m + n is equal to .
62
For a 3 3 matrix M: |adj M| = |M|2 and |kM| = k3|M|.
|2A| = 23 6 = 48 = 24 3
|adj(2A)| = 482 = 28 32
Let B = A2 adj(2A): |B| = 62 28 32 = 210 34
|3 adj B| = 33|B|2 = 33 220 38 = 220 311
|adj(3 adj B)| = (220 311)2 = 240 322
m = 40, n = 22
m + n = 62
Answer: 62
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