Question

If A is a square matrix such that A²=A, then (I + A)² – 3A is

Answer 1

Given: A is a square matrix such that A²=A

To find: The value of (I + A)² – 3A

Solution:

• Now we have given that A² = A.

• We have also given the term (I + A)² – 3A

• First expanding the given term, we get:

              (I + A)² – 3A = I^2 + A^2 + 2(IA) - 3A

• Now we know the property IA = A and I^2 = I.

• So applying it, we get:

              I + A + 2A - 3A

              I + 3A - 3A

              I

Answer:

          So the value of (I + A)² – 3A is I.

Answer 2

Answer:

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