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Matrices and Determinants question

2019 · Shift 1 · Q29
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Matrices and Determinants question

2019 · Shift 1 · Q29

JEE AdvancedMathematicsMatrices and DeterminantsMultiple correct+4 / −1
Let M=[01a1233b1]M = \left[ {\begin{matrix} 0 & 1 & a \\ 1 & 2 & 3 \\ 3 & b & 1 \\ \end{matrix} } \right]M=​013​12b​a31​​ and adj M=[−11−18−62−53−1]M = \left[ {\begin{matrix} { - 1} & 1 & { - 1} \\ 8 & { - 6} & 2 \\ { - 5} & 3 & { - 1} \\ \end{matrix} } \right]M=​−18−5​1−63​−12−1​​ where a and b are real numbers. Which of the following options is/are correct?
  1. A
    det(adj M2) = 81
  2. B
    If M[αβγ]=[123]M\left[ {\begin{matrix} \alpha \\ \beta \\ \gamma \\ \end{matrix} } \right] = \left[ {\begin{matrix} 1 \\ 2 \\ 3 \\ \end{matrix} } \right]M​αβγ​​=​123​​, then α−β+γ=3\alpha - \beta + \gamma = 3α−β+γ=3
  3. C
    (adj M)−1+adj M−1=−M{(adj\,M)^{ - 1}} + adj\,{M^{ - 1}} = - M(adjM)−1+adjM−1=−M
  4. D
    a + b = 3
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