Question

What is \[A^{-1}\] when \[|A|=9\] and \[\operatorname{adj}A=\begin{bmatrix}7&-3&2\\3&0&-3\\-1&3&1\end{bmatrix}\]?

विकल्प

• \[9\begin{bmatrix}7&-3&2\\3&0&-3\\-1&3&1\end{bmatrix}\]

• \[\frac19\begin{bmatrix}7&-3&2\\3&0&-3\\-1&3&1\end{bmatrix}\]

• \[-\frac19\begin{bmatrix}7&-3&2\\3&0&-3\\-1&3&1\end{bmatrix}\]

• \[\frac1{9}\begin{bmatrix}1&1&1\\0&1&3\\1&-2&1\end{bmatrix}\]

Answer 1

The inverse formula is \[A^{-1}=\frac1{|A|}\operatorname{adj}(A).\] Since \(|A|=9\), every entry of \(\operatorname{adj}A\) is multiplied by \(\frac19\).