If \(A=\begin{bmatrix}1 & -1 & 1\\1 & -2 & -2\\2 & 1 & 3\end{bmatrix}\) and square matrix B satisfy AB = 8I, then the value of |B| is:
Answer & explanation
Correct answer: option 2
\(A=\begin{vmatrix}1 & -1 & 1\\1 & -2 & -2\\2 & 1 & 3\end{vmatrix}\)
$|A|=1(-4)+1(7)+1(5)$
$=8$
$AB=8I$
$|AB|=|8I|$
$⇒|B|=\frac{8^3}{8}=\frac{8×8×8}{8}=64$