Let $A$ be an invertible $10\times 10$ matrix with real entries such that the sum of each row is $1$. Then choose the correct option.
- The sum of the entries of each row of the inverse of $A$ is $1$.
- The sum of the entries of each column of the inverse of $ A$ is $1$.
- The trace of the inverse of $A$ is non-zero.
- None of the above.
If the matrix is given we can find its inverse but how can we find its inverse if the matrix itself not given?
Any idea on how to find the answer?
Best Answer
HINT:
What would happen if you multiplied this matrix by $\pmatrix{1 \\ 1 \\ \vdots \\ 1}$? What does this tell you?