Determinants — Practice Quiz
ICSE · Class 12 · Mathematics
Try a 4-question quiz on Determinants for ICSE Class 12 Mathematics: tap an answer to check it and see why. 100 questions in the full chapter test.
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Quick Quiz: Determinants
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The determinant of a 2×2 matrix [[3,5],[2,4]] is:
For a square matrix A of order 3, |kA| equals:
If two rows of a determinant are identical, then the value of the determinant is:
The cofactor C₁₁ of element 5 in matrix [[5,3],[2,4]] is:
Sample Questions
Every rectangular matrix has a determinant.
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False
Determinants are defined only for square matrices. Rectangular matrices (m×n with m≠n) do not have determinants.
For matrices A and B of the same order, |AB| equals:
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|A| × |B|
The product rule for determinants: |AB| = |A|·|B|. This is a fundamental property of determinants.
The value of |A| = |Aᵀ| for any square matrix A.
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True
Transposing a matrix does not change its determinant: |Aᵀ| = |A|. This is because determinant expansion by rows equals expansion by columns.
For a non-singular matrix A, A⁻¹ equals:
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(adj A)/|A|
A⁻¹ = (1/|A|) × adj A = (adj A)/|A|. This requires |A| ≠ 0 (non-singular).
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