Question

Find the inverse of matrix [3-1-10 9]

Answer 1

`\mathbf A=\begin{bmatrix}3&-1\\-10&9\end{bmatrix}`

The inverse is given by


`\mathbf A^(-1)=\frac1{\det\mathbf A}\mathrm{adj}\,\mathbf A`

where
`\det\mathbf A` is the determinant of the matrix, and
`\mathrm adj\,\mathbf A` is the adjugate matrix, or transpose of the cofactor matrix.


`\det\mathbf A=\begin{vmatrix}3&-1\\-10&9\end{vmatrix}=3(9)-(-1)(-10)=17`


`\mathrm{adj}\,\mathbf A=\begin{bmatrix}9&10\\1&3\end{bmatrix}^\top=\begin{bmatrix}9&1\\10&3\end{bmatrix}`

So the inverse is


`\mathbf A^(-1)=\frac1{17}\begin{bmatrix}9&1\\10&3\end{bmatrix}`

Answer 2

C. [ 9/17 1/17 ]

[10/17 3/17 ]