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If A and B are symmetric matrices then AB-BA is a _______.

Question

If $A$ and $B$ are symmetric matrices then
$A B - B A$ is a _______.

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A

and

B

are symmetric matrices then

A B - B A

is a _______.

7 mins ago

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Text solutionVerified

A B - B A

is a skew symmetric matrix.

A

and

B

are symmetric matrices.

∴ A^{'} = A, B^{'} = B

Now,

[A B - B A]^{'} = (A B)^{'} - (B A)^{'}

= B^{'} A^{'} - A^{'} B^{'} \dots\dots [∵ (A B)^{'} = B^{'} A^{'}]

= B A - A B \dots\dots {∵ A^{'} = A

and

B^{'} = B}

= - [A B - B A]

So,

[A B - B A]

is a skew symmetric matrix.

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Question Text	If $A$ and $B$ are symmetric matrices then $A B - B A$ is a _______.
Answer Type	Text solution:1
Upvotes	150