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To find the value of |2A|, where A is a non-singular (invertible) matrix of order 3 such that A² = 2A, we can use the properties of determinants.

First, let's write down the equation A² = 2A. We can rewrite this equation as:

A² - 2A = 0

Now, factor out A from the left side of the equation:

A(A - 2I) = 0

Where I is the identity matrix of the same order as A.

Since A is non-singular, it means that A - 2I must be the zero matrix, because if A - 2I were invertible, we could multiply both sides of the equation by its inverse to get A = 0, which would contradict the assumption that A is non-singular.

So, we have:

A - 2I = 0

Now, let's solve for A:

A = 2I

Now, we can find |2A|:

|2A| = |2I|

Since the determinant of the identity matrix I of any order is 1, we have:

|2I| = 2³ × |I| = 8 * 1 = 8

So, the value of |2A| is:

b) 8

Given

A²= 2A

Taking Determinant both sides

|A² | = |2A|

|A × A| = |2A|

|A||A| = |2A|

Since order of matrix is 3, using [kA] = k" |A|

|A||A| = 2³|A|

|A||A| = 8|A||

|A||A|8|A|=0

|A| (|A| -8)=0

Thus, |A|0 or |A| = 8

Given that A is a non-singular matrix,

..|A|= 8

Now,

|2A|=2³|A|

= 8×8

= 64

So, the correct answer is (C) = 64