Q. 46

Without expanding, prove that .

Answer :

Let


We know that the sign of a determinant changes if any two rows or columns are interchanged.


By interchanging R1 and R2, we get



By interchanging R2 and R3, we get




Hence,


Let us once again consider


By interchanging R1 and R2, we get



By interchanging C1 and C2, we get




Recall that the value of a determinant remains same if it its rows and columns are interchanged.



Hence,


Thus,


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Determinants of Matrices of different orderDeterminants of Matrices of different orderDeterminants of Matrices of different order59 mins
Types of Matrices & PropertiesTypes of Matrices & PropertiesTypes of Matrices & Properties51 mins
Determining a determinantDetermining a determinantDetermining a determinant63 mins
Triangular Matrices & operations on matricesTriangular Matrices & operations on matricesTriangular Matrices & operations on matrices58 mins
Know About finding the Adjoint & Inverse Of MatrixKnow About finding the Adjoint & Inverse Of MatrixKnow About finding the Adjoint & Inverse Of Matrix46 mins
Interactive Quiz on Properties of DeterminantsInteractive Quiz on Properties of DeterminantsInteractive Quiz on Properties of Determinants43 mins
Lecture on Product of DeterminantsLecture on Product of DeterminantsLecture on Product of Determinants58 mins
Test Yourself, Properties of DeterminantsTest Yourself, Properties of DeterminantsTest Yourself, Properties of Determinants30 mins
Interactive Quiz on Matrices & DeterminantsInteractive Quiz on Matrices & DeterminantsInteractive Quiz on Matrices & Determinants48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses