If A is skew symmetric matrix of order 3, then the value of |A| isa)3b)0c)9d)27Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Skew Symmetric Matrix:

A skew symmetric matrix is a square matrix whose transpose is equal to its negative. In other words, for a skew symmetric matrix A of order 3, we have A^T = -A.

Determinant of Skew Symmetric Matrix:

For a skew symmetric matrix of order 3, the determinant |A| is calculated as follows:
|A| = det(A) = det(A^T) = det(-A) = (-1)^3 * det(A) = -det(A)

Since the determinant of a skew symmetric matrix is equal to the negative of its determinant, we have |A| = -|A|.

Value of |A| for a Skew Symmetric Matrix of Order 3:

Given that A is a skew symmetric matrix of order 3, we know that |A| = -|A|. This implies that |A| = 0, as any number multiplied by its negative is 0.

Therefore, the value of |A| for a skew symmetric matrix of order 3 is 0, making option 'B' the correct answer.

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