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

It is given that A = [[2, 3], [4, 1]]
Hence, A² = [[2, 3], [4, 1]] [[2, 3], [4, 1]] = [[16, 9], [12, 13]]
Now, 3A² = [[48, 27], [36, 39]]
12A = [[24, 36], [48, 12]]
Consider, 3A² + 12A = [[48, 27], [36, 39]] + [[24, 36], [48, 12]] = [[72, 63], [84, 51]]
Therefore, 3A² + 12A = [[72, 63], [84, 51]]
Hence, adj(3A² + 12A) = [[51, -63], [-84, 72]] = [[51, -63], [-84, 72]]
The determinant of 3A²+12A is (72)(51) - (63)(84) = 3672 - 5292 = -1620
Then adj(3A²+12A) = [[51, -63], [-84, 72]]