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in Mathematics by (64.8k points)

If A = [(3, -2), (4, -2)] and I = [(1, 0), (0, 1)], find k so that A2 = kA - 2I

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Given than A2 = kA – 2I

By definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get 

3k − 2 = 1  k = 1 

−2k = −2  k = 1 

4k = 4  k = 1 

−4 = −2k − 2  k = 1 

Hence, k = 1

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