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  • Need solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 31

Need solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 31

Answers (1)

Answer:

 (AB - BA) is skew symmetric matrix

Hint:

 Use the concept of symmetric and skew-symmetric Metrix.

Given:

 A and B are symmetric.

Solution:

Since, A and B are symmetric.

\begin{aligned} &(A B-B A)^{\prime}=(A B)^{\prime}-(B A)^{\prime}=B^{\prime} A^{\prime}-A^{\prime} B^{\prime} \\ &=B A-A B=-(A B-B A) \\ &(A B-B A)^{\prime}=-(A B-B A) \\ &A B-B A \end{aligned}

So, (AB - BA)  is skew symmetric matrix

Posted by

Gurleen Kaur

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