JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 1
Let $A=[a_{ij}]$ be a real matrix of order $3\times3$, such that $a_{i1}+a_{i2}+a_{i3}=1$, for $i=1,2,3$. Then, the sum of all the entries of the matrix $A^{3}$ is equal to :
Matrices
Solution
Row sums equal $1$ means $A\mathbf{1}=\mathbf{1}$ with $\mathbf 1=(1,1,1)^T$. Then $A^3\mathbf1=\mathbf1$, so each row of $A^3$ sums to $1$. Total of entries $=3$. Option (C).