CBSE Class 12 Sample Paper for 2024 Boards

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Question 2 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at August 14, 2026 by

If A and B are invertible square matrices of the same order, then which of the following is not correct?

(a) |AB^(-1) |=(|A|)/(|B|)Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β  (b) |(AB)^(-1) |=1/(|A||B|)

(c) (AB)^(-1)=B^(-1) A^(-1)Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β (d) (A+B)^(-1)=B^(-1)+A^(-1)

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[Class 12] If A and B are invertible square matrices of the same order - CBSE Class 12 Sample Paper for 2024 Boards

part 2 - Question 2 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12
part 3 - Question 2 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12 part 4 - Question 2 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Transcript

Let’s dicuss each option one by one Option (a) - |〖𝑨𝑩〗^(βˆ’πŸ) |=(|𝑨|)/(|𝑩|) Solving LHS |〖𝐴𝐡〗^(βˆ’1) |=|𝐴||𝐡^(βˆ’1) | = |𝐴| 1/(|𝐡|) = (|𝐴|)/(|𝐡|) So, option (a) is correct Option (b) - |(𝑨𝑩)^(βˆ’πŸ) |=𝟏/(|𝑨||𝑩|) Solving L.H.S |γ€–(𝐴𝐡)γ€—^(βˆ’1) | = | 𝐡^(βˆ’1) 𝐴^(βˆ’1)| = | 𝑩^(βˆ’πŸ) γ€–| |𝑨〗^(βˆ’πŸ)| = 1/(|𝐡|) 1/(|𝐴|) = 𝟏/(|𝑨||𝑩|) = R.H.S So, option (b) is correct Option (c) - (𝐴𝐡)^(βˆ’1)=𝐡^(βˆ’1) 𝐴^(βˆ’1) This is a correct property. So, option (c) is correct Option (d) - (𝑨+𝑩)^(βˆ’πŸ)=𝑩^(βˆ’πŸ)+𝑨^(βˆ’πŸ) Let’s check this with the help of an example Let’s consider A = [β– (1&3@0&2)] and B = [β– (2&1@1&2)] Since L.H.L β‰  R.H.L Thus, (𝐴+𝐡)^(βˆ’1)≠𝐡^(βˆ’1)+𝐴^(βˆ’1) ∴ So, option (d) is incorrect So, the correct answer is (d)

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