Q.30 Matrix A =
[ 0   6 ]
[ p   0 ]
will be skew-symmetric when p = _____.

Skew Symmetric Matrix Example: Find p for Matrix A

Matrix A =

[ 0   6 ]
[ p   0 ]

is skew-symmetric when p = -6.

Step-by-Step Solution

A skew-symmetric matrix satisfies A^T = −A, where A^T is the transpose of A.

The transpose of A is:

[ 0   p ]
[ 6   0 ]

The negative transpose is:

[ 0   −p ]
[ −6   0 ]

Equating Elements

• (1,2): 6 = −p → p = −6
• (2,1): p = −6 confirms consistency
• Diagonal entries are already zero

The skew-symmetric matrix p value problem asks when Matrix A becomes skew-symmetric.

Core Properties

• A^T = −A
• Diagonal entries are zero
• Off-diagonal: a_ij = −a_ji

Solving 6 = −p gives p = −6.

Exam Relevance

Common in IIT JAM, JEE, and Class 12 exams. A = [0 6; −6 0] satisfies skew-symmetry fully.