If A = [ * 20 c 4&1 3&2 ]and I = [ * 20 c 1&0 0&1 ], A^2 - 6A = - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right]$and $I = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$, ${A^2} - 6A = $

A
$3I$
B
$5I$
✓
$-5I$
D
None of these

✓

Answer

Correct option: C.

$-5I$

c
(c) ${A^2} - 6\,A = \left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right] - 6\left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{c}}{19}&6\\{18}&7\end{array}} \right] - \left[ {\begin{array}{*{20}{c}}{24}&6\\{18}&{12}\end{array}} \right]$$\left[ {\begin{array}{*{20}{c}}{ - 5}&0\\0&{ - 5}\end{array}} \right] = - 5I$.

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