SCALAR MATRIX, Matrices I have read two definitions of scalar matrix. The first one is that a square  matrix whose principal diagonal elements are some nonzero scalar is called scalar matrix. But the second is slightly different which says a square matrix whose  diagonal elements all contain the same scalar. In the second definition, it has not been mentioned that the scalar is nonzero. Which one is correct? Please clear my confusion.

A scalar matrix is a diagonal matrix whose diagonal elements all contain the same scalar $k\in\mathbb{R}$; that is, a matrix of the form $kI$, $I$ being the identity matrix.
The special case $k=0$ implies the $0$ matrix, but this would still be scalar. Thus, I coincide with your second definition.
