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Determinants

Question

Evaluate: $[\begin{matrix} a + ib & c + id \\ - c + id & a - ib \end{matrix}]$

Solution

$[\begin{matrix} a + ib & c + id \\ - c + id & a - ib \end{matrix}] = (a + ib) (a - ib) - (c + id) (- c + id) = (a^{2} - i^{2} b^{2}) - (- c^{2} + i^{2} d^{2}) = (a^{2} + b^{2}) - (- c^{2} - d^{2}) . . . . . . . . . (∵ i^{2} = - 1) = a^{2} + b^{2} + c^{2} + d^{2})$

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Determinants

Evaluate: $[\begin{matrix} a + ib & c + id \\ - c + id & a - ib \end{matrix}]$

Some More Questions From Determinants Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Determinants

Evaluate: a + ibc + id-c + ida - ib

Some More Questions From Determinants Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Evaluate: $[\begin{matrix} a + ib & c + id \\ - c + id & a - ib \end{matrix}]$