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प्रश्न
If matrix A = [aij]2×2, where aij `{:(= 1 "if i" ≠ "j"),(= 0 "if i" = "j"):}` then A2 is equal to ______.
विकल्प
I
A
0
None of these
उत्तर
If matrix A = [aij]2×2, where aij `{:(= 1 "if i" ≠ "j"),(= 0 "if i" = "j"):}` then A2 is equal to I.
Explanation:
Given that A = [aij]2×2
Let A = `[("a"_11, "a"_12),("a"_21, "a"_22)]_(2 x 2)`
a11 = 0 ....[∵ i = j]
a12 = 1 ....[∵ i ≠ j]
a21 = 1 ....[∵ i ≠ j]
a22 = 0 ....[∵ i = j]
∴ A = `[(0, 1),(1, 0)]`
Now, A2 = A . A
= `[(0,1),(1,0)] [(0, 1),(1, 0)]`
=`[(0 + 1, 0 + 0),(0 +0, 1 + 0)]`
= I
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