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BITSAT 2009
Exam
BITSAT
Year
2009
Subject
Mathematics
Chapter
Sequences and Series

BITSAT 2009 · Mathematics · Sequences and Series

If A and B are (2 × 2) matrices, then which of the following is...

If AA and BB are (2 \times 2) matrices, then which of the following is true?

Options

  1. A((\mathrm{A}+\mathrm{B})^2=\mathrm{A}^2+\mathrm{B}^2+2 AB\mathrm{AB})
  2. B(A−B)2=A2+B2−2AB(A-B)^2=A²+B²-2 A B
  3. C(A−B)(A+B)=A2+AB−BA−B2(A-B)(A+B)=A²+A B-B A-B²
  4. D(A−B)(A+B)=A2−B2(A-B)(A+B)=A²-B²

Correct answer

C. (A−B)(A+B)=A2+AB−BA−B2(A-B)(A+B)=A²+A B-B A-B²

Step-by-step solution

For two (2 \times 2) matrices, (A \& B) (A−B)×(A+B)=A×A+A×B−B×A−B×B=A2−B2+AB−BA\begin{aligned} & (A-B) \times(A+B) \\ & =A \times A+A \times B-B \times A-B \times B \\ & =A²-B²+A B-B A \end{aligned}) Hence, (A−B)(A+B)=A2+AB−BA−B2(A-B)(A+B)=A²+A B-B A-B²$
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