Algebra

Matrices & Determinants

Medium

core

If $A$ is a skew-symmetric matrix of order 5, then $|adjA|$ is equal to

-1

-5

✅ Correct Option: 2

$A$ is a skew-symmetric matrix of order 5.

This means $A$ is a $5 \times 5$ matrix where $A^T = -A$ (transpose of $A$ equals negative of $A$ ).

For any skew-symmetric matrix of odd order, the determinant is always 0.

Since $A^T = -A$ , taking determinant on both sides:

$|A^T| = |-A|$

Using the properties $|A^T| = |A|$ and $|-A| = (-1)^5 \times |A| = -|A|$ for a $5 \times 5$ matrix:

$|A| = -|A|$

$2|A| = 0$

$|A| = 0$

For any $n \times n$ matrix $A$ :

$|adj A| = |A|^{n-1}$

For the given matrix:

$n = 5$

$|A| = 0$

$|adj A| = (0)^{5-1}$

$|adj A| = 0^4$

$|adj A| = 0$

Therefore, $|adj A| = 0$

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Which one of the following options is incorrect?

For a square matrix A in the matrix equation AX = B.

If AAA is a skew-symmetric matrix of order 5, then ∣adjA∣|adjA|∣adjA∣ is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A$ is a skew-symmetric matrix of order 5, then $|adjA|$ is equal to