If A = [[3, 1], [−1, 2]], then A² − 5A + 7I is equal to:

If A = [[3, 1], [−1, 2]], then A² − 5A + 7I is equal to:

• A. [[0, 0], [0, 0]]
• B. [[1, 0], [0, 1]]
• C. [[−1, 0], [0, −1]]
• D. [[7, 0], [0, 7]]

Answer: A) [[0, 0], [0, 0]]

Explanation: A² = [[3×3+1×(−1), 3×1+1×2], [−1×3+2×(−1), −1×1+2×2]] = [[9−1, 3+2], [−3−2, −1+4]] = [[8, 5], [−5, 3]]. 5A = [[15, 5], [−5, 10]]. 7I = [[7, 0], [0, 7]]. A² − 5A + 7I = [[8−15+7, 5−5+0], [−5+5+0, 3−10+7]] = [[0, 0], [0, 0]].