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Question:

If matrix A = [1 1; 1 1] and A² = KA, then write the value of K.

Solution:

If A = [1 1; 1 1], then A² can be computed as shown below:
A² = [1 1; 1 1] * [1 1; 1 1] = [11 + 11, 11 + 11; 11 + 11, 11 + 11] = [2 2; 2 2]
Since A² = KA, therefore, [2 2; 2 2] = K[1 1; 1 1]
[2 2; 2 2] = [K K; K K]
Now equating the matrices we get K = 2.
Hence, K = 2.