If A = [0100], then A2023 is equal to ______. - Mathematics

Question

If A = $[\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}]$ , then A²⁰²³ is equal to ______.

Options

$[\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}]$
$[\begin{matrix} 0 & 2023 \\ 0 & 0 \end{matrix}]$
$[\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}]$
$[\begin{matrix} 2023 & 0 \\ 0 & 2023 \end{matrix}]$

MCQ

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Solution

If A = $[\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}]$ , then A²⁰²³ is equal to $\underset{̲}{[\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}]}$ .

Explanation:

Given:

A = $[\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}]$

A² = A.A

= $[\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}] [\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}]$

= $[\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}]$

A³ = A².A

= $[\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] [\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}]$

= $[\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}]$

Similarly, A²⁰²³ = $[\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}]$

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