Which of the following statements is incorrect for a square matrix $A$ where $|A| \neq 0$?
- AIf $A$ is a diagonal matrix,$A^{-1}$ will also be a diagonal matrix.
- BIf $A$ is a symmetric matrix,$A^{-1}$ will also be a symmetric matrix.
- CIf $A^{-1} = A$,then $A$ is an idempotent matrix.
- DIf $A^{-1} = A$,then $A$ is an involutory matrix.
Explore More
Similar Questions
If $A$ is a $3 \times 3$ matrix and $|A|=2$,then $|\operatorname{Adj}(\operatorname{Adj} A)| \operatorname{Adj}(\operatorname{Adj} A) = $ (in $A$)
Suppose $A$ is any $3 \times 3$ non-singular matrix and $(A-3 I)(A-5 I)=O$,where $I=I_3$ and $O=O_3$. Here $O_3$ represents the zero matrix of order $3$ and $I_3$ is the identity matrix of order $3$. If $\alpha A+\beta A^{-1}=4 I$,then $\alpha+\beta$ is equal to:
Let $A$ be a $3 \times 3$ matrix and $B$ be its adjoint matrix. If $|B|=64,$ then $|A|$ is equal to
If $A, B$ and $(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1}))$ are non-singular matrices of the same order,then the inverse of $A(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1}))^{-1}B$ is equal to
DifficultJEE MAIN 2025
View SolutionIf $A$ is a square matrix of order $3$ such that $\operatorname{det}(A)=3$ and $\operatorname{det}\left(\operatorname{adj}\left(-4 \operatorname{adj}\left(-3 \operatorname{adj}\left(3 \operatorname{adj}\left((2A)^{-1}\right)\right)\right)\right)\right)=2^{m} 3^{n}$,then $m+2n$ is equal to:
DifficultJEE MAIN 2024
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