Question

If the matrix A is both symmetric and skew symmetric, then A. A is a diagonal matrix B. A is a zero matrix C. A is a square matrix D. None of these

Answer 1

It is given that the matrix A is a symmetric matrix.

A ′ =A(1)

It is also given that matrix A is skew-symmetric matrix.

A ′ =−A(2)

Solve both the equations (1) and (2).

A=−A A+A=O 2A=O A=O

The matrix A is a zero matrix or null matrix.

Thus, out of all the four options, option (B) is correct.