Home
Class 11
MATHS
Let A be a non-singular square matrix of...

Let A be a non-singular square matrix of order n. Then; `|adjA| = |A|^(n-1)`

A

Statement -1 is True, Statement -2 is true, Statement -2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement -2 is True, Statement -2 is not a correct explanation for Statement -1.

C

Statement -1 is True, Statement -2 is False.

D

Statement -1 is False, Statement -2 is True.

Text Solution

Verified by Experts

The correct Answer is:
C
We know that
`A(adj A) =absAI`
`:. Abs(A(adjA))=abs(absAI)-absA^nabsA [:' abs(kA)=k^nabsA]`
`rArr absA abs(adjA)=absA^n`
`rArr abs(adjA)=absA^(n-1)`
So, statement -1 is true. But, Statement -2 is false. Because,`abs(kA)=k^nabsA`.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Exercise|80 Videos

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|57 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|21 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

Let A be a non-singular square matrix of order 3xx3 . Then |adjA| is equal to

Let A be a non-singular square matrix of order 3 xx 3. Then |adj A| is equal to (a) |A| (B) |A|^2 (C) |A|^3 (D) 3|A|

If A and adj A are non-singular square matrices of order n, then adj (A^(-1))=

If A is a non-singular matrix of order nxxn, then : |adj*A|=

If A is a non-singular matrix of order 3, then |adjA^(3)|=

If A is a non-singular matrix of order n, then A(adj A)=

If A is non-singular matrix of order, nxxn,

Let A be a square matrix of order n. Then; A(adjA)=|A|I_(n)=(adjA)A

If A is a non-singlular square matrix of order n, then the rank of A is