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Question:

If matrix A = [2 2; 2 2] and A² = pA, then write the value of p.

Solution:

If A = [2 2; 2 2], then A² can be computed as shown below:
A² = [2 2; 2 2] * [2 2; 2 2] = [22 + 22, 22 + 22; 22 + 22, 22 + 22] = [8 8; 8 8]
Since A² = pA, therefore, [8 8; 8 8] = p[2 2; 2 2] = [2p 2p; 2p 2p]
Now equating the matrices we get 2p = 8 => p = 4.
Hence, p = 4.