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:

512 64 32 8

64

\(A=\begin{vmatrix}1 & -1 & 1\\1 & -2 & -2\\2 & 1 & 3\end{vmatrix}\) $|A|=1(-4)+1(7)+1(5)$ $=8$ $AB=8I$ $|AB|=|8I|$ $⇒|B|=\frac{8^3}{8}=\frac{8×8×8}{8}=64$