We are given with matrix A, such that

We need to verify A² + A = A(A + I).

Take L.H.S: A² + A.

Solve for A².

A² = A.A

Multiply 1^st row of matrix A by matching members of 1^st column of matrix A, then sum them up.

(1, 0, -1)(1, 2, 0) = (1 × 1) + (0 × 2) + (-1 × 0)

⇒ (1, 0, -1)(1, 2, 0) = 1 + 0 + 0

⇒ (1, 0, -1)(1, 2, 0) = 1

Similarly, repeat steps to fill for the other elements.

Now, add A² and A,

Take R.H.S: A(A + I)

First, let us solve for (A + I).

Multiply (A + I) from A.

Since, L.H.S = R.H.S.

Thus, (A² + A) = A(A + I).