If \( A=\begin{bmatrix}2 & 1\\ 7 & 5\end{bmatrix} \), then the value of \( |A(adjA)| \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9
The determinant of A is
\( \displaystyle |A|=2\cdot5-1\cdot7 \)
\( \displaystyle =3 \)
By the property \( A\,(\mathrm{adj}\,A)=|A|\,I \),
\( \displaystyle A(\mathrm{adj}\,A)=3I \)
\( \displaystyle =\begin{bmatrix}3&0\\0&3\end{bmatrix} \)
Hence
\( \displaystyle |A(\mathrm{adj}\,A)|=9 \)
Shortcut: In general
\( \displaystyle |A(\mathrm{adj}\,A)|=|A|\cdot|\mathrm{adj}\,A|=|A|^{n} \)
Here n = 2 and |A| = 3, so the value is \( 3^{2}=9 \).