Question

If A = $\left[\begin{array}{ccc}2& 1& 1\\ 1& 2& 1\\ 1& 1& 2\end{array}\right]$ then det (Adj A) =

• A. 4
• B. 16
• C. 8
• D. 2

Answer 1

The correct option is B 16

det (Adj A) $=|A{|}^{n-1}$ {where n is order of matrix}

det A$=2[4-1]-1[2-1]+1[1-2]$$=6-1-1=4.\Rightarrow |A|=4$
det (Adj A) $=|A{|}^{n-1}$$=4^{3-1}$$=16$
so (b)