If A = [ * 20 c 4&2 - 1 &1 ]and I is the identity matrix of order… - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}4&2\\{ - 1}&1\end{array}} \right]$and $I$ is the identity matrix of order $2$, then $(A - 2I)(A - 3I) = $

A
$I$
✓
$O$
C
$\left[ {\begin{array}{*{20}{c}}1&0\\0&0\end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}}0&0\\0&1\end{array}} \right]$

✓

Answer

Correct option: B.

$O$

b
(b) $(A - 2I)\,(A - 3I) = \left[ {\begin{array}{*{20}{c}}2&2\\{ - 1}&{ - 1}\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&2\\{ - 1}&{ - 2}\end{array}} \right]\, = \,\left[ {\begin{array}{*{20}{c}}0&0\\0&0\end{array}} \right] = O$.

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