Home
Class 12
MATHS
If A and B are 3xx3 matrices and abs(A)n...

If A and B are `3xx3` matrices and `abs(A)ne 0,` which of the
following are true?

A

`abs(AB)=0rArr abs(B) = 0`

B

`abs(AB)=0rArr B = 0`

C

`abs(A^(-1) ) = abs(A)^-1`

D

`abs(A+A) = 2 abs(A)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`abs(AB) = 0 rArr abs(A) abs(B) = 0`
`therefore abs(B) = 0 " as "abs(A) ne 0`
Also, `abs(A^(-1)) = abs(A)^(-1)`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|16 Videos

  • MATRICES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • MATRICES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|29 Videos

Similar Questions

Explore conceptually related problems

Which of the following are true: \ (2xx3)! =2!xx3!

If A and B are square matrices of same order, then which of the following is true -

If AB=A and BA=B then which of the following is/are true ?

If D_(1) and D_(2) are two 3xx3 diagonal matrices, then which of the following is/are true ?

If A and B are invertible matrices of same order, then which of the following statement is not true ?

If ab > 0 , then which one of the following must be true?

If the matrix A and B are of 3xx3 and (I-AB) is invertible, then which of the following statement is/are correct ?

If A and B are two square matrices such that AB=I, then which of the following is not true?

Let A and B be matrices of order 3 xx 3. If AB = 0, then which of the following can be concluded?

A and B be 3xx3 matrices such that AB+A+B=0 , then