Assume ,
, ,
prove that .
Proof : According to the properties of the determinant , perform the operation on , and transform into the lower triangular determinant , which is recorded as
;
Operate on , and transform into the lower triangular determinant form, which is recorded as
.
In this way, perform the operation on the first rows of , and then perform the same operation on the last columns as on , that is, convert into the lower triangular determinant :
,
so
.
