Home
Class 12
MATHS
If B is a non-singular matrix and A is a...

If B is a non-singular matrix and A is a square matrix, then `det (B^(-1) AB)` is equal to (A) `det (A^(-1))` (B) `det (B^(-1))` (C) `det (A)` (D) `det (B)`

Text Solution

Verified by Experts

Given, B is a non-singular matrix and A is a square matrix,
`det (B^(-1) AB)`
=`det (B^(-1) BA)`
=`det (I_n A)`
=`det (A)`
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos
  • ALGEBRA OF MATRICES

    RD SHARMA|Exercise Solved Examples And Exercises|410 Videos

Similar Questions

Explore conceptually related problems

If B is a non-singular matrix and A is a square matrix, then the value of det (B^(-1) AB) is equal to :

If x is a non singular matrix and y is a square matrix,such that det(x^(-1)yx)=K det y ,then find K

If is a non-singular matrix, then det (A^(1))=

if A is a square matrix such that A^(2)=A, then det (A) is equal to

If A is an invertible matrix of order 2, then det (A^(-1)) is equal to

If A is an invertible matrix of order 2 then det (A^(-1)) is equal to (a) det (A) (b) (1)/(det(A))(c)1 (d) 0

If A is invertible matrix. Then what is det (A^(-1)) equal to ?

If A is a 3x3 matrix and det(3A)=k{det(A)},k is equal to