If then verify that A² + A = (A + I), where I is the identity matrix.

Given

We need to prove A² + A = A (A + I).

Let us evaluate the LHS and the RHS one at a time.

To find the LHS, we will first calculate A².

We know A² = A × A

Now, the LHS is A² + A.

To find the RHS, we will first calculate A + I.

Now, the RHS is A(A + I).

Thus, A² + A = A (A + I).