Given A - 2 1- 2 1 - I is a unit matrix of order 2- Find all possible matrix X in XA - I

The correct option is A X does not existGiven A =[ 2 amp; 1; 2 amp;1 ]; . I is a unit matrix of order 2 . XA = I ⇒ X= ...

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Byju's Answer

Standard XII

Mathematics

Singular and Non Singualar Matrices

Given A =[ ...

Question

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

X

does not exist

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A^{- 1}

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A

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1 / A

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Solution

The correct option is A $X$ does not exist
Given $A = [\begin{matrix} 2 & 1 2 & 1 \end{matrix}];$ . $I$ is a unit matrix of order $2$ .
$X A = I$
$\Rightarrow X = A^{- 1}$
but $| A | = ∣ ∣ ∣ \begin{matrix} 2 & 1 2 & 1 \end{matrix} ∣ ∣ ∣ = 0$
$∴ A^{- 1}$ does not exist.
Hence, no $X$ is possible such that $X A = I$ .
Hence, option A is correct.

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Given A=[2121]. I is a unit matrix of order 2. Find all possible matrix X in XA=I

The correct option is A X does not existGiven A=[2121]; . I is a unit matrix of order2.XA=I⇒X=A−1but |A|=∣∣∣2121∣∣∣=0∴A−1 does not exist.Hence, no X is possible such that XA=I.Hence, option A is correct.

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