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If A = [[2, -3], [-4, 1]], then adj(3A² + 12A) is equal to:

1. [[72, -63], [-84, 51]]
2. [[72, -84], [-63, 51]]
3. [[51, 63], [84, 72]]
4. [[84, 72], [63, 51]]

Correct answer: [[51, 63], [84, 72]]

Solution

A^2 = [[16,-9],[-12,13]], so 3A^2+12A = [[48,-27],[-36,39]] + [[24,-36],[-48,12]] = [[72,-63],[-84,51]]. adj of [[a,b],[c,d]] = [[d,-b],[-c,a]] = [[51,63],[84,72]].

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