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Addition and Subtraction of a Matrix

Given A=[2 ...

Question

Given $A = [\begin{matrix} 2 & 1 1 & 1 \end{matrix}]$ . $I$ is a unit matrix of order $2$ . Find all possible matrix $X$ such that $A X = I$

X

does not exist

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X

is a unit matrix

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X

is a identity matrix

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None of these

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Solution

The correct option is D None of these
$A = [\begin{matrix} 2 & 1 1 & 1 \end{matrix}]$
Here, $| A | = 1 \neq 0$
Hence, $A^{- 1}$ exists.
Given $A X = I$
$\Rightarrow X = A^{- 1}$
Now, $a d j A = C^{T} = {[\begin{matrix} 1 & - 1 - 1 & 2 \end{matrix}]}^{T}$
$\Rightarrow a d j A = [\begin{matrix} 1 & - 1 - 1 & 2 \end{matrix}]$
Hence, $A^{- 1} = [\begin{matrix} 1 & - 1 - 1 & 2 \end{matrix}]$
So, $X = [\begin{matrix} 1 & - 1 - 1 & 2 \end{matrix}]$

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Given A=[2111].I is a unit matrix of order 2. Find all possible matrix X such that AX=I

The correct option is D None of theseA=[2111]Here, |A|=1≠0Hence, A−1 exists.Given AX=I⇒X=A−1Now, adjA=CT=[1−1−12]T⇒adjA=[1−1−12]Hence, A−1=[1−1−12]So, X=[1−1−12]

Given $A = [\begin{matrix} 2 & 1 1 & 1 \end{matrix}]$ . $I$ is a unit matrix of order $2$ . Find all possible matrix $X$ such that $A X = I$