Mark the correct alternative in the following:
If A and B are square matrices or order 2, then det (A + B) = 0 is possible only when
We are given that,
Matrices A and B are square matrices.
Order of matrix A = 2
Order of matrix B = 2
Det (A + B) = 0
We need to find the condition at which det (A + B) = 0.
Let,
Matrix A = [aij]
Matrix B = [bij]
Since their orders are same, we can express matrices A and B as
A + B = [aij + bij]
⇒ |A + B| = |aij + bij| …(i)
Also, we know that
Det (A + B) = 0
That is, |A + B| = 0
From (i),
|aij + bij| = 0
If
⇒ [aij + bij] = 0
Each corresponding element is 0.
⇒ A + B = 0
Thus, det (A + B) = 0 is possible when A + B = 0 .