If A = [[1, 2], [−1, 1]] (rows), then the value of A² − 2A + 2I is equal toयदि A = [[1, 2], [−1, 1]] (पंक्तियाँ) एक आव्यूह है, तब A² − 2A + 2I का मान है

Explanation

A² = [[1−2, 2+2], [−1−1, −2+1]] = [[−1, 4], [−2, −1]]. Then A² − 2A = [[−1−2, 4−4], [−2+2, −1−2]] = [[−3, 0], [0, −3]], and adding 2I gives [[−1, 0], [0, −1]] = −I.A² = [[1−2, 2+2], [−1−1, −2+1]] = [[−1, 4], [−2, −1]]। तब A² − 2A = [[−1−2, 4−4], [−2+2, −1−2]] = [[−3, 0], [0, −3]], और 2I जोड़ने पर [[−1, 0], [0, −1]] = −I।