Question

If A is a square matrix of order 3 and |-5A| = k|A|, then what is the
value of k?

Answer 1

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.

Step-by-step explanation:

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