If Matrix A = 1 2 4 3 such that A X = I , then X = ________

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Question: Answered & Verified by Expert

If Matrix

A = [\begin{matrix} 1 & 2 \\ 4 & 3 \end{matrix}]

such that

A X = I,

then

X =

________

MathematicsMatricesMHT CETMHT CET 2016

Options:

A $\frac{1}{5} [\begin{matrix} 1 & 3 \\ 2 & - 1 \end{matrix}]$
B $\frac{1}{5} [\begin{matrix} 4 & 2 \\ 4 & - 1 \end{matrix}]$
C $\frac{1}{5} [\begin{matrix} - 3 & 2 \\ 4 & - 1 \end{matrix}]$
D $\frac{1}{5} [\begin{matrix} - 1 & 2 \\ - 1 & 4 \end{matrix}]$

Solution:

2854 Upvotes Verified Answer

The correct answer is:

\frac{1}{5} [\begin{matrix} - 3 & 2 \\ 4 & - 1 \end{matrix}]

Given

A X = I

∴ X = A^{- 1}

= \frac{1}{|A|} adj A

∴ X = - \frac{1}{5} [\begin{matrix} 3 & - 2 \\ - 4 & 1 \end{matrix}]

∴ X = \frac{1}{5} [\begin{matrix} - 3 & 2 \\ 4 & - 1 \end{matrix}]

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