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If A and B are symmetric matrices of the same order, then (ABt - BAt) is

If A and B are symmetric matrices of the same order, then (ABt - BAt) is Correct Answer skew symmetric

CONCEPT:

Symmetric Matrix:

Any real square matrix A = (aij) is said to be symmetric matrix if and only if aij = aji, ∀ i and j or in other words we can say that if A is a real square matrix such that A = At then A is said to be a symmetric matrix.

Skew-symmetric Matrix:

Any real square matrix A = (aij) is said to be skew-symmetric matrix if and only if aij = - aji, ∀ i and j or in other words we can say that if A is a real square matrix such that A = - At then A is said to be a skew-symmetric matrix.

Note: If A and B are matrices of same order m × n, then (A ± B)t = At ± Bt and (AB)t = Bt × At.

CALCULATION:

Given: A and B are symmetric matrices of the same order

As we know that, if any real square matrix A = (aij) is said to be symmetric matrix if and only if aij = aji, ∀ i and j or in other words we can say that if A is a real square matrix such that A = At then A is said to be a symmetric matrix.

i.e A = At and B = Bt

As we know that, if A and B are matrices of same order m × n, then (A ± B)t = At ± Bt and (AB)t = Bt × At.

⇒ (ABt - BAt)t = (ABt)t - (BAt)t

⇒ (ABt - BAt)t = BAt - ABt

⇒ (ABt - BAt)t = - (ABt - BAt)

So, (ABt - BAt) is a skew symmetric matrix.

Hence, option C is the correct answer.

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