If A and B are symmetric matrices of the same order then (AB – BA) i

1.	If A and B are symmetric matrices of the same order then (AB – BA) is always A. a symmetric matrix B. a skew-symmetric matrix C. a zero matrix D. an identity matrix
Answer» Given A and B are symmetric matrices A’ = A --- 1 B’ = B ---- 2 Now (AB – BA)’ = (AB)’ – (BA)’ = B’A’ – A’B’ [∵(AB) ’ = B’A’ ] = BA – AB [Using 1 and 2] ∴(AB – BA)’ = - (AB - BA) AB-BA is a skew symmetric matrix.

If A and B are symmetric matrices of the same order then (AB – BA) is always A. a symmetric matrix B. a skew-symmetric matrix C. a zero matrix D. an identity matrix

Answer»

Given A and B are symmetric matrices

A’ = A --- 1

B’ = B ---- 2

Now (AB – BA)’ = (AB)’ – (BA)’

= B’A’ – A’B’

[∵(AB) ’ = B’A’ ]

= BA – AB [Using 1 and 2]

∴(AB – BA)’ = - (AB - BA)

AB-BA is a skew symmetric matrix.