Question:

The inverse of the matrix $\begin{bmatrix} {5}&{-2}\\ {3}&{1}\\ \end{bmatrix}$ is is

Updated On: May 17, 2024
  • $\frac {1}{11}\begin{bmatrix} {1}&{2}\\ {-3}&{5}\\ \end{bmatrix} $
  • $\begin{bmatrix} {1}&{2}\\ {-3}&{5}\\ \end{bmatrix} $
  • $\frac {1}{13}\begin{bmatrix} {-2}&{5}\\ {1}&{3}\\ \end{bmatrix} $
  • $\begin{bmatrix} {1}&{3}\\ {-2}&{5}\\ \end{bmatrix} $
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The Correct Option is A

Solution and Explanation

Let $A=\begin{bmatrix}5 & -2 \\ 3 & 1\end{bmatrix}$ $|A|=5+6=11$ and $adj\, A=\begin{bmatrix}1 & 2 \\ -3 & 5\end{bmatrix}$ $A^{-1}=\frac{1}{|A|}$ (adj A) $=\frac{1}{11}\begin{bmatrix}1 & 2 \\ -3 & 5\end{bmatrix}$
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Concepts Used:

Invertible matrices

A matrix for which matrix inversion operation exists, given that it satisfies the requisite conditions is known as an invertible matrix. Any given square matrix A of order n × n is called invertible if and only if there exists, another n × n square matrix B such that, AB = BA = In, where In  is an identity matrix of order n × n.

For example,

It can be observed that the determinant of the following matrices is non-zero.