# Inverse of a diagonal non-singular matrix is:

$A.$ Symmetric matrix

$B.$ Skew-symmetric matrix

$C.$ Diagonal matrix

$D.$ Scalar matrix

Last updated date: 21st Mar 2023

•

Total views: 309.3k

•

Views today: 3.87k

Answer

Verified

309.3k+ views

Hint: - Just consider the cases given by taking an example in mind to solve such problems. These questions don’t need lots of working.

Taking an example of a diagonal matrix and finding its inverse we check the following result.

$A = \left( {\begin{array}{*{20}{c}}

2&0&0 \\

0&3&0 \\

0&0&4

\end{array}} \right)$ Where $A$is a diagonal matrix.

${A^{ - 1}} = \left( {\begin{array}{*{20}{c}}

{\dfrac{1}{2}}&0&0 \\

0&{\dfrac{1}{3}}&0 \\

0&0&{\dfrac{1}{4}}

\end{array}} \right)$ and${A^{ - 1}}$ is the inverse of a diagonal matrix.

We find by an example that the inverse of a diagonal matrix is also a diagonal matrix.

Inverse of a nonsingular diagonal matrix is a nonsingular diagonal matrix with all the diagonal elements inverted. Therefore, the resultant invertible matrix is a diagonal matrix.

So the correct option is C.

Note: In linear algebra, a diagonal matrix has values of entries outside the main diagonal as zero; the term usually refers to a square matrix. In the above question it is easier to check the results by example rather than going by finding formulae.

Taking an example of a diagonal matrix and finding its inverse we check the following result.

$A = \left( {\begin{array}{*{20}{c}}

2&0&0 \\

0&3&0 \\

0&0&4

\end{array}} \right)$ Where $A$is a diagonal matrix.

${A^{ - 1}} = \left( {\begin{array}{*{20}{c}}

{\dfrac{1}{2}}&0&0 \\

0&{\dfrac{1}{3}}&0 \\

0&0&{\dfrac{1}{4}}

\end{array}} \right)$ and${A^{ - 1}}$ is the inverse of a diagonal matrix.

We find by an example that the inverse of a diagonal matrix is also a diagonal matrix.

Inverse of a nonsingular diagonal matrix is a nonsingular diagonal matrix with all the diagonal elements inverted. Therefore, the resultant invertible matrix is a diagonal matrix.

So the correct option is C.

Note: In linear algebra, a diagonal matrix has values of entries outside the main diagonal as zero; the term usually refers to a square matrix. In the above question it is easier to check the results by example rather than going by finding formulae.

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

What is the Full Form of PVC, PET, HDPE, LDPE, PP and PS ?

Alfred Wallace worked in A Galapagos Island B Australian class 12 biology CBSE

Imagine an atom made up of a proton and a hypothetical class 12 chemistry CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

How do you define least count for Vernier Calipers class 12 physics CBSE

Why is the cell called the structural and functional class 12 biology CBSE

A 30 solution of H2O2 is marketed as 100 volume hydrogen class 11 chemistry JEE_Main