For a matrix

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

For a

3\times 3

matrix

A

, suppose

|A|=12

and

\text{adj}\,A=\begin{pmatrix}4 & -2 & 8\\ 1 & 0 & -3\\ 5 & 2 & -1\end{pmatrix}.

Which of the following matrices is

A^{-1}

? (a)

\begin{pmatrix}\frac{2}{3} & -\frac{1}{3} & \frac{4}{3}\\ \frac{1}{6} & 0 & -\frac{1}{2}\\ \frac{5}{6} & \frac{1}{3} & -\frac{1}{6}\end{pmatrix}

(b)

\begin{pmatrix}\frac{1}{3} & \frac{1}{12} & \frac{5}{12}\\ -\frac{1}{6} & 0 & \frac{1}{6}\\ \frac{2}{3} & -\frac{1}{4} & -\frac{1}{12}\end{pmatrix}

(c)

\begin{pmatrix}\frac{1}{3} & -\frac{1}{6} & \frac{2}{3}\\ \frac{1}{12} & 0 & -\frac{1}{4}\\ \frac{5}{12} & \frac{1}{6} & -\frac{1}{12}\end{pmatrix}

(d)

\begin{pmatrix}\frac{1}{36} & -\frac{1}{72} & \frac{1}{18}\\ \frac{1}{144} & 0 & -\frac{1}{48}\\ \frac{5}{144} & \frac{1}{72} & -\frac{1}{144}\end{pmatrix}