If A is a square matrix of order 3 and |-5A| = k|A|, then what is the
value of k?
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Answer:
The value of k is 8.
Let A is a square matrix of order 3.
According to the property of determinant:
|cA|=c^3|A|∣cA∣=c3∣A∣
Where, c is a constant.
The value of 2|A| is
|2A|=2^3|A|∣2A∣=23∣A∣
|2A|=8|A|∣2A∣=8∣A∣ ...(1)
It is given that
|2A|=k|A|∣2A∣=k∣A∣ ...(2)
From (1) and (2), we get
k=8k=8
Therefore the value of k is 8.
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