Home
Class 12
MATHS
If A and B are n-rowed unitary matrices,...

If A and B are n-rowed unitary matrices,then AB and BA are also unitary matrices.

Text Solution

Verified by Experts

A and B are two orthogonal matrices. Hence,
`A^(T)A=A A^(T)=I` and `B B^(T)=B^(T)B=I`
AB will be orthogonal if
`(AB)^(T) (AB)=(B^(T)A^(T)) (AB)`
`=B^(T) (A^(T)A)B`
`=B^(T) IB`
`=B^(T)B=I`
Similarly, we can show that `(BA)^(T) (BA)=I`. Therefore, Ba is also orthogonal.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise 13.5|17 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Single)|65 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.3|10 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

If A and B are two matrices such that AB=B and BA=A, then

If A and B are two n-rowed square matrices such that AB=O and B is non-singular. Then

Assertion (A) : If A and B are symmetric matrices, then AB - BA is a skew symmetric matrix Reason (R) : (AB)' = B' A'

If A and B are 3times3 matrices such that AB=A and BA=B, then

If A and B are symmetric matrices of same order, then AB - BA is a :

If A and B are two matrices such that A+B =AB , then

If A and B are two square matrices such that AB=A and BA=B , then A^(2) equals

If A and B are symmetric matrices then AB-BA is a Symmetric Matrix (b) Skewl symmetric matrix Diagonal matrix (d) Null matrix