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Represent A as a sum of a unity matrix with another matrix B: A = 1 + B.
Then, use the formula for the squared sum: A^2 = (1 + B)^2.
B^2 will give a zero matrix.
Then, multiple the result by A.
You will get 1 + 3B, etc.
Eventually, you will get A^100 = 1+100B, which in turn will give you the result.
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Linear Algebra Foundations #5 - The 100th Power of a Matrix
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Represent A as a sum of a unity matrix with another matrix B: A = 1 + B. Then, use the formula for the squared sum: A^2 = (1 + B)^2. B^2 will give a zero matrix. Then, multiple the result by A. You will get 1 + 3B, etc. Eventually, you will get A^100 = 1+100B, which in turn will give you the result.