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Mathematics Question on Symmetric and Skew Symmetric Matrices

If the matrix [23 5−1]\begin{bmatrix} 2 & 3 \\\ 5 & -1 \end{bmatrix}= A + B, where A is symmetric and B is skew-symmetric then B =

A

[10 01]\begin{bmatrix} 1 & 0 \\\ 0 & 1 \end{bmatrix}

B

[0−1 10]\begin{bmatrix} 0 & -1 \\\ 1 & 0 \end{bmatrix}

C

[0−1 −10]\begin{bmatrix} 0 & -1 \\\ -1 & 0 \end{bmatrix}

D

[−10 01]\begin{bmatrix} -1 & 0 \\\ 0 & 1 \end{bmatrix}

Answer

[0−1 10]\begin{bmatrix} 0 & -1 \\\ 1 & 0 \end{bmatrix}

Explanation

Solution

The correct option is (B) : [0−1 10]\begin{bmatrix} 0 & -1 \\\ 1 & 0 \end{bmatrix}.