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Mathematics II20755 marksNumerical: matrix commutativityMatrix operations

Let A and B be matrices. What value(s) of k if any will make AB = BA?

Let A and B be matrices. What value(s) of k if any will make AB = BA?

$$A = \begin{bmatrix} -1 & -2 \ 5 & 9 \end{bmatrix}, \quad B = \begin{bmatrix} 9 & 2 \ k & -1 \end{bmatrix}$$

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$$A = \begin{bmatrix} -1 & -2 \ 5 & 9 \end{bmatrix}, \quad B = \begin{bmatrix} 9 & 2 \ k & -1 \end{bmatrix}$$ Requirement: $AB = BA$. $$AB = \begin{bmatrix} (-1)(9)+(-2)(k) & (-1)(2)+(-2)(-1) \ (5)(9)+(9)(k) & (5)(2)+(9)(-1) \end{bmatrix} = \begin{bmatrix} -9-2k & 0 \ 45+9k & 1 \end{bmatrix}

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