Question:medium
If \( A = \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix} \), then \( A^n + nI \) is equal to:
If \( A = \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix} \), then \( A^n + nI \) is equal to:
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For matrices of the form \( \begin{pmatrix} 1 & 0 k & 1 \end{pmatrix} \), the \( n \)-th power is simply \( \begin{pmatrix} 1 & 0 nk & 1 \end{pmatrix} \). This is a very common shortcut in entrance exams.
Updated On: May 1, 2026
- \( I \)
- \( nA \)
- \( I + nA \)
- \( I - nA \)
- \( nA - I \)
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The Correct Option is C
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