Consider the following statements :
$(a)$ If any two rows or columns of a determinant are identical,then the value of the determinant is zero.
$(b)$ If the corresponding rows and columns of a determinant are interchanged,then the value of the determinant does not change.
$(c)$ If any two rows (or columns) of a determinant are interchanged,then the value of the determinant changes in sign.
Which of these are correct?
$(a)$ If any two rows or columns of a determinant are identical,then the value of the determinant is zero.
$(b)$ If the corresponding rows and columns of a determinant are interchanged,then the value of the determinant does not change.
$(c)$ If any two rows (or columns) of a determinant are interchanged,then the value of the determinant changes in sign.
Which of these are correct?
- A$(a)$ and $(b)$
- B$(b)$ and $(c)$
- C$(a)$ and $(c)$
- D$(a)$,$(b)$ and $(c)$
Explore More
Similar Questions
The value of the determinant $\left|\begin{array}{ccc}\sin \alpha & \cos \alpha & \sin (\alpha+\delta) \\ \sin \beta & \cos \beta & \sin (\beta+\delta) \\ \sin \gamma & \cos \gamma & \sin (\gamma+\delta)\end{array}\right|$ is equal to
MediumKCET 2011
View SolutionIf $A$ is any square matrix of order $3 \times 3$,then $|3A|$ is equal to:
The determinant $\left| {\begin{array}{*{20}{c}}{{a^2} + {x^2}}&{ab}&{ca}\\{ab}&{{b^2} + {x^2}}&{bc}\\{ca}&{bc}&{{c^2} + {x^2}}\end{array}} \right|$ is a divisor of:
Difficult
View SolutionIf $x, y, z \in \mathbb{R}$,then the value of the determinant $\left|\begin{array}{lll}\left(5^{x}+5^{-x}\right)^{2} & \left(5^{x}-5^{-x}\right)^{2} & 1 \\ \left(6^{x}+6^{-x}\right)^{2} & \left(6^{x}-6^{-x}\right)^{2} & 1 \\ \left(7^{x}+7^{-x}\right)^{2} & \left(7^{x}-7^{-x}\right)^{2} & 1\end{array}\right|$ is:
MediumKCET 2018
View Solution$\left| {\begin{array}{ccc} a - b - c & 2a & 2a \\ 2b & b - c - a & 2b \\ 2c & 2c & c - a - b \end{array}} \right| = $
Difficult
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo