Find two non-zero matrices and with integer entries such that AB-BA= bmatrix 0 & 3 -3…

MATHEMATICS · Subjective · CBSE · Mathematics · Matrices · Matrices

Problem

Find two non-zero 2×22\times2 matrices AA and BB with integer entries such that AB−BA=[03−30].AB-BA=\begin{bmatrix}0 & 3\\-3 & 0\end{bmatrix}. (i) Exhibit one suitable pair (A,B)(A,B) and verify through explicit calculation that it satisfies the above condition. (ii) Justify that no choice of scalar (multiple of the identity) matrices can satisfy the given relation, thereby confirming that genuinely different matrices are required.

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