Engineering
Mathematics
Introduction to Determinants
Question

Consider the following statements:
(1) Determinant is a square matrix.
(2) Determinant is a number associated with a square matrix.
Which of the above statements is/are correct?

2 only

Both 1 and 2

Neither 1 nor 2

1 only

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Solution
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A determinant is not a matrix itself, but a scalar value computed from a square matrix. Statement (1) is incorrect because the determinant is a number, not a matrix. Statement (2) is correct; it is a unique number associated with a square matrix. For a 2x2 matrix A=abcd, its determinant is det(A)=ad-bc.

Final Answer: 2 only