Multiply scalar ' 0 ' with an n×n matrix A Scalar multiplication of a matrix is obtained by multiplying each element of the matrix by that scalar.
Let A be an n×n matrix
Then, 0⋅A=00.⎡⎢
⎢⎣a11a12……a1n⋮an1an2……ann⎤⎥
⎥⎦
=⎡⎢
⎢⎣00……0⋮00……0⎤⎥
⎥⎦
=0
Hence, the product of any matrix by the scalar 0 is the null matrix.