Let A, B and C be 2 × 2 matrices with entries from the set of real numbers. Define * as…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
Let A, B and C be 2 × 2 matrices with entries from the set of real numbers. Define * as follows :
\(\mathrm{A}^{*} \mathrm{~B}=\frac{1}{2}\left(\mathrm{AB}^{\prime}+\mathrm{A}^{\prime} \mathrm{B}\right)\)
\(\mathrm{A}^{*} \mathrm{~B}=\frac{1}{2}\left(\mathrm{AB}^{\prime}+\mathrm{A}^{\prime} \mathrm{B}\right)\)
- A * B = B * A
- A * A = A2
- A * (B + C) = A * B + A * C
- A * I = A + A’
Answer
(C) A * (B + C) = A * B + A * C
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