If A = [[2, 1], [1, 2]], then A² − 4A + 3I is equal to:
If A = [[2, 1], [1, 2]], then A² − 4A + 3I is equal to:
- A. 0
- B. I
- C. 2I
- D. 3I
Answer: A) 0
Explanation: A² = [[2, 1], [1, 2]] × [[2, 1], [1, 2]] = [[4+1, 2+2], [2+2, 1+4]] = [[5, 4], [4, 5]]. 4A = [[8, 4], [4, 8]]. 3I = [[3, 0], [0, 3]]. A² − 4A + 3I = [[5−8+3, 4−4+0], [4−4+0, 5−8+3]] = [[0, 0], [0, 0]] = 0.
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