If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C = A + B ? - Mathematics MCQ Mathematics Mock Test - 3 2026 | ExamTest.live

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If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C = A + B ?

Solution & Step-by-step Explanation

For identity matrix I, I^{T} = I .So B = A^{T} = A = I . C = A + B = I + I = 2 I C = 200020002 The determinant ∣ C ∣ = 2 \times 2 \times 2 = 8 .

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If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C = A + B ?

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8

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