(A) Given that $A$ is a non-singular matrix,its determinant $|A| \neq 0$,which implies that the inverse matrix $A^{-1}$ exists. Given the equation $AB

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) Given that $A$ is a non-singular matrix,its determinant $|A| \neq 0$,which implies that the inverse matrix $A^{-1}$ exists. Given the equation $AB = O$,where $O$ is the zero matrix. Multiplying both sides by $A^{-1}$ on the left: $A^{-1}(AB) = A^{-1}O$ $(A^{-1}A)B = O$ $IB = O$ $B = O$ Therefore,$B$ must be a null matrix.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Types of matrices, Algebra of matrices

Medium

If $A$ and $B$ are square matrices of order $3 \times 3$,$A$ is non-singular,and $AB = O$,then $B$ is a:

AP EAMCET 2002 All AP EAMCET

TS EAMCET 2002 All TS EAMCET

A
null matrix
B
non-singular matrix
C
singular matrix
D
unit matrix

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

3 and 4 .Determinants and Matrices

Subtopic

Types of matrices, Algebra of matrices

Previous Year

AP EAMCET 2002 Paper All AP EAMCET years →

Previous Year

TS EAMCET 2002 Paper All TS EAMCET years →

Suppose $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is a real matrix with non-zero entries,$ad - bc = 0$ and $A^2 = A$. Then,$a + d$ equals

DifficultKVPY 2018

View Solution

If $2X - \begin{bmatrix} 1 & 2 \\ 7 & 4 \end{bmatrix} = \begin{bmatrix} 3 & 2 \\ 0 & -2 \end{bmatrix}$,then $X$ is equal to

Easy

View Solution

If $A$ and $B$ are two matrices such that $A+B$ and $AB$ are both defined,then

Medium

View Solution

Let $A$ be a square matrix such that $a_{ij} \in \{-1, 0, 1\}$ for all $i, j$ and it has exactly one non-zero entry in each row as well as in each column. Then:

Difficult

View Solution

The matrix $A = \left[ {\begin{array}{*{20}{c}}0&{ - 4}&1\\4&0&{ - 5}\\{ - 1}&5&0\end{array}} \right]$ is:

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $A$ and $B$ are square matrices of order $3 \times 3$,$A$ is non-singular,and $AB = O$,then $B$ is a:

Similar Questions

Suppose $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is a real matrix with non-zero entries,$ad - bc = 0$ and $A^2 = A$. Then,$a + d$ equals

If $2X - \begin{bmatrix} 1 & 2 \\ 7 & 4 \end{bmatrix} = \begin{bmatrix} 3 & 2 \\ 0 & -2 \end{bmatrix}$,then $X$ is equal to

If $A$ and $B$ are two matrices such that $A+B$ and $AB$ are both defined,then

Let $A$ be a square matrix such that $a_{ij} \in \{-1, 0, 1\}$ for all $i, j$ and it has exactly one non-zero entry in each row as well as in each column. Then:

The matrix $A = \left[ {\begin{array}{*{20}{c}}0&{ - 4}&1\\4&0&{ - 5}\\{ - 1}&5&0\end{array}} \right]$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module