Question

Assertion :If A, B, C are matrices such that $|A_{3\times 3}|=3,|B_{3\times 3}|=-1$, and $|C_{2\times 2}|=+2$, then $|2ABC|=-12$. Reason: For matrices A, B, C of the same order, $|ABC|=|A||B||C|$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Given $|A_{3\times 3}|=3,|B_{3\times 3}|=-1,|C_{2\times 2}|=2$

As C is of different order from A and B , we cant multiply them to get the product of $|ABC|$.

Hence the Assertion given is wrong.

For matrix $A,B,C$ of same order $|ABC|=|A||B||C|$.

Hence the reason is correct.