If A=\begin{bmatrix}1&0&0\\ 0&1&0\\ 0&0&1\end{bmatrix}, then what is 23A^3-19A^2-4A equal to?
- A. Null matrix of order 3 ✓
- B. Identity matrix of order 3
- C. \begin{bmatrix}2&0&0\\ 0&2&0\\ 0&0&2\end{bmatrix}
- D. \begin{bmatrix}7&0&0\\ 0&7&0\\ 0&0&7\end{bmatrix}
Correct Answer: A. Null matrix of order 3
Explanation
Here, A is the identity matrix I. For any integer n, I^n = I. Substituting this into the expression gives 23I - 19I - 4I = 0 \cdot I, which is the null matrix of order 3.
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