Find the $2 imes 2$ matrix X such that $X\begin{pmatrix} 3 & 1 \ 5 & 2 \end{pmatrix} = \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}$.

Question

Find the $2 	imes 2$ matrix X such that $X\begin{pmatrix} 3 & 1 \ 5 & 2 \end{pmatrix} = \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}$.

Accepted Answer

$\begin{pmatrix} 2 & -1 \ -5 & 3 \end{pmatrix}$. The equation XA = I means X = A⁻¹. For A = [[3,1],[5,2]], det(A) = (3)(2)-(1)(5) = 6-5 = 1. The inverse is (1/1)×[[2,-1],[-5,3]] = [[2,-1],[-5,3]]. Option B is the negative of the correct inverse, C omits the sign changes, and D transposes the diagonal without adjusting signs.

Answer

A) $\begin{pmatrix} 2 & -1 \ -5 & 3 \end{pmatrix}$

Answer

B) $\begin{pmatrix} -2 & 1 \ 5 & -3 \end{pmatrix}$

Answer

C) $\begin{pmatrix} 2 & 1 \ 5 & 3 \end{pmatrix}$

Answer

D) $\begin{pmatrix} 3 & -1 \ -5 & 2 \end{pmatrix}$

Find the $2 \times 2$ matrix X such that $X\begin{pmatrix} 3 & 1 \\ 5 & 2 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$.

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