Maths. Section AMatrices (Section A)

If A and B are square matrices of same order, then A'B - B'A is a:

If A and B are square matrices of same order, then \(A'B - B'A\) is a:

Answer & explanation

Correct answer: option 1

The correct answer is Option (1) → Skew symmetric matrix

Let \(P = A'B - B'A\). Take the transpose, using \((XY)' = Y'X'\) and \((X')' = X\):

    \(P' = (A'B)' - (B'A)'\)
    \(= B'(A')' - A'(B')'\)
    \(= B'A - A'B\)
    \(= -P\)

A square matrix with \(P' = -P\) is skew symmetric. So A′B − B′A is a skew symmetric matrix.