Question

The negative of a matrix is obtained by multiplying it by

Answer 1

Take scalar $-1$ and multiply it with $n\times n$matrix A
Let A be a $n\times n$ matrix
Then,

$-1\cdot A=-1\cdot \left[\begin{array}{ccc}{a}_{11}& a_{12}\dots \dots \dots & a_{1n}\\ ⋮& & \\ a_{n1}& a_{n2}\dots \dots & a_{nn}\end{array}\right]$

$=\left[\begin{array}{ccc}-a_{11}& -a_{12}\cdots \cdots & -a_{1n}\\ ⋮& & \\ -a_{n1}& -a_{n2\cdots \cdots }\cdots & -a_{nn}\end{array}\right]$

$=-A$
Hence, the negative of a matrix is obtained by multiplying it by $-1$.