Home
Class 12
MATHS
If A is an invertible matrix of order ...

If `A` is an invertible matrix of order 3, then which of the following is not true (a) `|a d j\ A|=|A|^2` (b) `(A^(-1))^(-1)=A` (c) If `B A=C A` , then `B!=C` , where `B` and `C` are square matrices of order 3 (d) `(A B)^(-1)=B^(-1)A^(-1)` , where `B=([b_(i j)])_(3xx3)` and `|B|!=0`

Text Solution

Verified by Experts

If `B A=C A` , then `B!=C` , where `B` and `C` are square matrices of order 3
if A is invertible matrix of order 3 then `A^(-1)` exists.
Now BA=AB
...
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 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 and B are invertible matrices, which of the following statement is not correct. a d j\ A=|A|A^(-1) (b) det(A^(-1))=(detA)^(-1) (c) (A+B)^(-1)=A^(-1)+B^(-1) (d) (A B)^(-1)=B^(-1)A^(-1)

For an invertible square matrix of order 3 with real entries A^-1=A^2 then det A= (A) 1/3 (B) 3 (C) 0 (D) 1

If A is a square matrix of order 3 and |A|=3 then |adjA| is (A) 3 ; (B) 9 ; (C) (1)/(3) ; (D) 0

Let A,B and C be square matrices of order 3xx3 with real elements. If A is invertible and (A-B)C=BA^(-1), then

Let A,B and C be square matrices of order 3xx3 with real elements. If A is invertible and (A-B)C=BA^(-1), then

If A is a matrix of order 3 and |A|=8 , then |a d j\ A|= (a) 1 (b) 2 (c) 2^3 (d) 2^6

If AneB, AB = BA and A^(2)=B^(2) , then the value of the determinant of matrix A+B is (where A and B are square matrices of order 3xx3 )

If A and B are two invertible matrices of same order, the (AB)^-1 is (A) AB (B) BA (C) B^-1A^-1 (D) does not exist

If A and B are invertible matrices of the same order then (A) Adj(AB)=(adjB)(adjA) (B) (A+B)^-1=A^-1+B^-1 (C) (AB)^-1=B^-1A^-1 (D) none of these