If A is square matrix of size 4 and |A| = 6. If |Adj.(Adj.(3A) | = 2a3b, then value of a + b is
Answer & explanation
Correct answer: option 2
$∴|Adj.(Adj.A)|=|A|^{(n-1)^2}$
$∴|Adj.(Adj.3A)|=|3A|^{3^2}$
$=(3^4|A|)^9$
$⇒3^{4×9}6^9$
$⇒3^{36}6^9⇒3^{36}.(2×3)^9⇒3^{36+9}.2^9$
$⇒3^{45}.2^9$ ⇒ a + b = 45 + 9 = 54
Option 2 is correct.