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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

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Solution

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.


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