A unit matrix is an integer matrix consisting of all 1s. The 
unit matrix is often denoted 
, or 
if 
.
Square unit matrices 
have determinant 0 for 
.
An 
unit matrix can be generated
in the Wolfram Language as ConstantArray[1,
m, n
].
Let 
be a commutative
ring with a multiplicative identity.
Then the term "unit matrix" is also used to refer to an 
square matrix 
with entries in 
for which there exists an 
square matrix 
such that
 |
with 
is the identity
matrix (MacDuffee 1943, p. 27; Marcus and Minc 1988, p. 69; Marcus
and Minc 1992, p. 42).
The term "unit matrix" is sometimes also used as a synonym for identity matrix (Akivis and Goldberg 1972, p. 71).
