Question

Inverse of a diagonal non-singular matrix is

• A. Symmetric matrix
• B. Skew-symmetric matrix
• C. Diagonal matrix
• D. Scalar matrix

Answer 1

The correct option is C Diagonal matrix

Let $D$ be an $n\times n$ diagonal non-singular matrix.

If any of the diagonal elements are zero, then $D$ is not invertible diagonal matrix.

Since $D$ is non-singular, we have none of the diagonal elements as zero.

Thus Inverse of a diagonal non-singular matrix is diagonal matrix.