Question

if A is a square matrix then A-A' will be

Answer 1

$\textbf{Concept used:}$

$\text{A square matrix A is said to be}\;\textbf{Skew symmetric}\;\text{if}\;A=-A'$

$\textbf{Given:}$

$\text{A is a square matrix}$

$\text{Consider,}$

$(A-A')'$

$=A'-(A')'$

$=A'-A$

$=-(A-A')$

$\implies\bf\,A-A'=-(A-A')'$

$\therefore\textbf{A-A' will be a skew symmetric matrix}$

Find more:

If A is square matrix, then which of the following is not true ? OPTIONS --- 1) AA' is symmetric 2) A-A' is skew symmetric. 3) A square is symmetric 4) A+A' is symmetric​

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