If A is a square matrix of order 4 and |A| = 4, then |2A| will be:
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When working with the determinant of a scalar multiple of a matrix, the key idea is that multiplying a matrix \(A\) by a scalar \(k\) results in the determinant being multiplied by \(k^n\), where \(n\) is the size of the matrix. This property helps simplify the calculation of determinants when the matrix is scaled by a constant. For a \(4 \times 4\) matrix, raising the scalar to the power of 4 is crucial for finding the correct result.
- 8
- 64
- 16
- 4
The Correct Option is B
Approach Solution - 1
Here, $|2A|$ = 24·\(\times\)4 = 64
Approach Solution -2
For an \(n \times n\) matrix, the determinant of a scalar multiple of the matrix is given by:
\[ |kA| = k^n \cdot |A| \]
Here, we are given that \(A\) is a \(4 \times 4\) matrix and we are asked to find \( |2A| \). Applying the formula:
\[ |2A| = 2^4 \cdot |A| \]
The determinant of \(2A\) is then:
\[ |2A| = 2^4 \cdot 4 = 16 \cdot 4 = 64 \]
Conclusion: Thus, \( |2A| = 64 \).
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