
In a skew-symmetric matrix, the diagonal elements are all
A) One
B) Zero
C) Different from each other
D) Non-zero
Answer
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Hint: A square matrix is said to be skew symmetric matrix if
or , that is for all possible values of and .
In transpose of a matrix, columns and rows are interchanged. Transpose denoted by: . For example:
If
Then
Complete step-by-step answer:
Step 1: Consider a square matrix
Where : row number and : column number.
Step 2: Condition for skew symmetric matrix:
Here, is transpose of matrix A
i.e.
Step 3: Now, if we put ,
We have,
for all .
Step 4: diagonal elements of a square matrix
In the square matrix
Elements are diagonal elements.
All the diagonal elements of the skew symmetric matrix are zero. Thus, the correct option is (B).
Note: Another way to understand the solution.
We have a theorem: Any square matrix A with real number entries, is a skew symmetric matrix.
Example question: The skew symmetric matrix of matrix .
In transpose of a matrix, columns and rows are interchanged. Transpose denoted by:
If
Then
Complete step-by-step answer:
Step 1: Consider a square matrix
Where
Step 2: Condition for skew symmetric matrix:
Here,
i.e.
Step 3: Now, if we put
We have,
Step 4: diagonal elements of a square matrix
In the square matrix
Elements
All the diagonal elements of the skew symmetric matrix are zero. Thus, the correct option is (B).
Note: Another way to understand the solution.
We have a theorem: Any square matrix A with real number entries,
Example question: The skew symmetric matrix of matrix
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