JEE Main 2014 · 11 Apr · Shift 1 · Mathematics Q64

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MathematicsSingle correct+4 / -1Question 64 of 90

Let A be a $3\times3$ matrix such that
$A\begin{bmatrix}1&2&3\\0&2&3\\0&1&1\end{bmatrix}=\begin{bmatrix}0&0&1\\1&0&0\\0&1&0\end{bmatrix}.$
Then $A^{-1}$ is :

\begin{bmatrix}3&1&2\\3&0&2\\1&0&1\end{bmatrix}

\begin{bmatrix}3&2&1\\3&2&0\\1&1&0\end{bmatrix}

\begin{bmatrix}0&1&3\\0&2&3\\1&1&1\end{bmatrix}

\begin{bmatrix}1&2&3\\0&1&1\\0&2&3\end{bmatrix}

Answer and worked solution

Official answer: A

$AM=P$ gives $A^{-1}=MP^{-1}=MP^{T}$ . Since $P$ is a permutation matrix, multiplying by $P^T$ reorders the columns of $M$ as (column 3, column 1, column 2):
$A^{-1}=\begin{bmatrix}3&1&2\\3&0&2\\1&0&1\end{bmatrix}.$

Topics:Adjoint and inverse Matrix algebra

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JEE Main 2014 · 11 Apr · Shift 1, Mathematics question 64