32:T7a1,Given that

A

3 \times 3

matrix and

|A|=2

33:T81d0,

\begin{aligned} & \text { Now, | 3adj }\left(|3 A| A^2\right) \text { | } \\\\ & =3^3\left|\operatorname{adj}\left(|3 A| A^2\right)\right| \\\\ & =3^3\left|\operatorname{adj}\left(54 A^2\right)\right| \\\\ & =3^3\left|54 A^2\right|^2 \\\\ & =3^3 \times\left(54^3\right)^2 \times|A|^4 \\\\ & =3^3 \times(54)^6 \times 2^4 ~~~~~ {[|A|=2 \text { given }]} \\\\ & =3^3 \times\left(3^3 \times 2\right)^6 \times 2^4 ~~~~~ {\left[\left(a^m\right)^n=a^{m n}\right]} \\\\ & =3^{11} \times 3^{10} \times 2^{10} ~~~~~~~ {\left[(a b)^m=a^m b^m\right]} \\\\ & =(3)^{11} \times(6)^{10} \end{aligned}

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