Question

Which of the following statements is not correct?

• A. A diagonal matrix has all diagonal elements equal to zero.
• B. A symmetric matrix \(A\) is a square matrix satisfying \(A' = A\).
• C. A skew symmetric matrix has all diagonal elements equal to zero.
• D. A row matrix has only one row.

Hint:

A diagonal matrix is a square matrix in which all off-diagonal elements are zero, but diagonal elements can be non-zero.

Answer 1

The Correct Option is A

- A diagonal matrix is a square matrix where all off-diagonal elements are zero. The diagonal elements can be non-zero. 

- A symmetric matrix \(A\) satisfies \(A' = A\), meaning it is equal to its transpose. 

- A skew symmetric matrix has all diagonal elements equal to zero. - A row matrix has only one row, as the name suggests. 

Thus, the statement "A diagonal matrix has all diagonal elements equal to zero" is false because the diagonal elements can be any value.