If $A$ is a $m \times n$matrix and $B$ is a matrix such that both $AB$ and $BA$ are defined, then the order of $B$ is
$m \times n$
$n \times m$
$m \times m$
$n \times n$
(b) It is obvious.
If $3X + 2Y = I$ and $2X – Y = O$, where $ I$ and $ O $ are unit and null matrices of order $3 $ respectively, then
Let $\alpha$ and $\beta$ be real numbers. Consider a $3 \times 3$ matrix $A$ such that $A ^2=3 A +\alpha I$. If $A ^4=21 A +\beta I$, then
Let $A=\left[a_{i j}\right]$ be a real matrix of order $3 \times 3$, such that $a_{i 1}+a_{i 2}+a_{i 3}=1$, for $i=1,2,3$. Then, the sum of all the entries of the matrix $A^{3}$ is equal to:
If the matrix $A=\left(\begin{array}{cc}0 & 2 \\ K & -1\end{array}\right)$ satisfies $A\left(A^{3}+3 I\right)=2 I$ then the value of $\mathrm{K}$ is :
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