Question

The inverse of a skew symmetric matrix (if it exists) is –

• A. A symmetric matrix
• B. A skew symmetric matrix
• C. A diagonal matrix
• D. None of these

Answer 1

Answer: (B)

A skew symmetric matrix

Answer 2

We have A¢ = –A

Now AA^–1 = A^–1 A = I_n

Ž (AA^–1)¢ = (A^–1A)¢ = (I_n)¢

Ž (A^–1)¢ A¢ = A¢ (A^–1)¢ = I_n

Ž (A^–1)¢ (–A) = (–A) (A^–1)¢ = I_nThus, (A^–1)¢ = – (A^–1) [inverse of a matrix is unique]