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3 and 4 .Determinants and Matrices
easy
જો $\mathrm{A}=\left[\begin{array}{rr}0 & -1 \\ 0 & 2\end{array}\right]$ અને $\mathrm{B}=\left[\begin{array}{ll}3 & 5 \\ 0 & 0\end{array}\right]$ તો $AB$ શોધો.
A
$\left[ {\begin{array}{*{20}{l}} 0&0 \\ 0&0 \end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{l}} 0&0 \\ 0&0 \end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{l}} 0&0 \\ 0&0 \end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{l}} 0&0 \\ 0&0 \end{array}} \right]$
Solution
We have $A B=\left[\begin{array}{rr}0 & -1 \\ 0 & 2\end{array}\right]\left[\begin{array}{ll}3 & 5 \\ 0 & 0\end{array}\right]=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$
Thus, if the product of two matrices is a zero matrix, it is not necessary that one of the matrices is a zero matrix.
Standard 12
Mathematics