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Question
If | A | = | kA |, where A is a square matrix of order 2, then sum of all possible values of k is ______.
Options
1
– 1
2
0
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Solution
If | A | = | kA |, where A is a square matrix of order 2, then sum of all possible values of k is 0.
Explanation:
Given,
| A | = | kA |
| A | = k2| A |
`\implies` k2 – 1 = 0
Then, k = 1 or – 1
∴ Sum of value of k = – 1 + 1 = 0.
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