If X = [ * 20 c 3& - 4 1& - 1 ], then the value of X^n is - Vidyadip

MCQ

If $X = \left[ {\begin{array}{*{20}{c}}3&{ - 4}\\1&{ - 1}\end{array}} \right]$, then the value of ${X^n}$ is

A
$\left[ {\begin{array}{*{20}{c}}{3n}&{ - 4n}\\n&{ - n}\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}{2 + n}&{5 - n}\\n&{ - n}\end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{c}}{{3^n}}&{{{( - 4)}^n}}\\{{1^n}}&{{{( - 1)}^n}}\end{array}} \right]$
✓
None of these

✓

Answer

Correct option: D.

None of these

d
(d) $X = \left[ {\begin{array}{*{20}{c}}3&{ - 4}\\1&{ - 1}\end{array}} \right] \Rightarrow {X^2} = \left[ {\begin{array}{*{20}{c}}5&{ - 8}\\2&{ - 3}\end{array}} \right]$.

Clearly for $n = 2$, the matrices in $(a), (b), (c)$ do not tally with $\left[ {\begin{array}{*{20}{c}}5&{ - 8}\\2&{ - 3}\end{array}} \right]$.

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