(C) Let $B = A - A^T$. To check if $B$ is symmetric or skew-symmetric,we find its transpose $B^T$.$B^T = (A - A^T)^T$Using the property $(X - Y)^T = X

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(C) Let $B = A - A^T$. To check if $B$ is symmetric or skew-symmetric,we find its transpose $B^T$.$B^T = (A - A^T)^T$Using the property $(X - Y)^T = X^T - Y^T$,we get:$B^T = A^T - (A^T)^T$Since $(A^T)^T = A$,we have:$B^T = A^T - A$$B^T = -(A - A^T)$$B^T = -B$Since $B^T = -B$,the matrix $A - A^T$ is a skew-symmetric matrix.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Special types of matrices, Transpose of matrices and Trace of matrices

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If $A$ is a square matrix and $A + A^T$ is a symmetric matrix,then $A - A^T$ is:

A
Unit matrix
B
Symmetric matrix
C
Skew symmetric matrix
D
Zero matrix

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3 and 4 .Determinants and Matrices

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Special types of matrices, Transpose of matrices and Trace of matrices

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Which of the following is a nilpotent matrix?

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If $A$ is a square matrix and $A + A^T$ is a symmetric matrix,then $A - A^T$ is:

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