यदि A= [ ll 1 & a 0 & 1 ] हो, तो A4 बराबर है-

MCQ

यदि $A=\left[\begin{array}{ll}1 & a \\ 0 & 1\end{array}\right]$ हो, तो A⁴ बराबर है-

A
$\left[\begin{array}{cc}1 & a^4 \\ 0 & 1\end{array}\right]$
B
$\left[\begin{array}{cc}4 & 4 a \\ 0 & 4\end{array}\right]$
C
$\left[\begin{array}{cc}4 & a^4 \\ 0 & 4\end{array}\right]$
✓
$\left[\begin{array}{cc}1 & 4 a \\ 0 & 1\end{array}\right]$

✓

Answer

Correct option: D.

$\left[\begin{array}{cc}1 & 4 a \\ 0 & 1\end{array}\right]$

(D) $\left[\begin{array}{cc}1 & 4 a \\ 0 & 1\end{array}\right]$
$\begin{array}{l} A ^2= A \cdot A =\left[\begin{array}{ll}1 & a \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}1 & a \\ 0 & 1\end{array}\right] \\ A ^2=\left[\begin{array}{cc}1 & 2 a \\ 0 & 1\end{array}\right]\end{array}$
$A ^4= A ^2 A^2=\left[\begin{array}{cc}1 & 2 a \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}1 & 2 a \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}1+0 & 2 a+2 a \\ 0+0 & 0+1\end{array}\right]$
$=\left[\begin{array}{cc}1 & 4 a \\ 0 & 1\end{array}\right]$
अतः सही विकल्प (D) है।

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