If A is square matrix of size 4 and |A| = 6. If |Adj.(Adj.(3A) | = 2a3b, then value of a + b is

24 54 72 216

54

$∴|Adj.(Adj.A)|=|A|^{(n-1)^2}$ $∴|Adj.(Adj.3A)|=|3A|^{3^2}$ $=(3^4|A|)^9$ $⇒3^{4×9}6^9$ $⇒3^{36}6^9⇒3^{36}.(2×3)^9⇒3^{36+9}.2^9$ $⇒3^{45}.2^9$ ⇒ a + b = 45 + 9 = 54 Option 2 is correct.