Answer :

To prove: AB – BA is a skew symmetric matrix.

*Symmetric matrix: A symmetric matrix is a square matrix that is equal to its transpose. In simple words, matrix A is symmetric if*

*A = A’*

*where A’ is the transpose of matrix A.*

*Skew Symmetric matrix: A skew* *symmetric matrix is a square matrix that is equal to minus of its transpose. In simple words, matrix A is skew symmetric if*

*A = -A’*

Given: A and B are symmetric matrices i.e.

A = A’ …(1)

B = B’ …(2)

Now calculating the transpose of AB – BA,

(AB – BA)’ = (AB)’ – (BA)’

(By property of transpose i.e. (A – B)’ = A’ – B’)

= B’A’ – A’B’

(By property of transpose i.e. (AB)’ = B’A’)

= BA – AB

= -(AB – BA)

Or we can say that: **(AB – BA) = - (AB – BA)’**

Clearly it satisfies the condition of skew symmetric matrix.

**Hence AB** **–** **BA is a skew symmetric matrix.**

Rate this question :

<span lang="EN-USMathematics - Exemplar

<span lang="EN-USMathematics - Exemplar

Fill in the blankMathematics - Exemplar

Fill in the blankMathematics - Exemplar

Fill in the blankMathematics - Exemplar

If A, B are squarMathematics - Exemplar

Fill in the blankMathematics - Exemplar

Fill in the blankMathematics - Exemplar

Express the folloMathematics - Board Papers

Fill in the blankMathematics - Exemplar