Question

Pick out the wrong statement. If \(A\) and \(B\) are square matrices of the same order, then

• A. \(A + B = B + A\)
• B. \((AB)' = B'A'\)
• C. \(A - B = I\)
• D. \(|AB| = |A||B|\)

Hint:

Only identities that hold for all matrices are universally true.

Answer 1

The Correct Option is C

Concept: Standard properties of matrices

Step 1: Check each statement
• (A) \(A + B = B + A\) \(\Rightarrow\) True (Matrix addition is commutative)
• (B) \((AB)' = B'A'\) \(\Rightarrow\) True (Transpose of product reverses order)
• (D) \(|AB| = |A||B|\) \(\Rightarrow\) True (Determinant property)

Step 2: Check statement (C) \[ A - B = I \]
• This is not a general identity
• It is true only for special matrices, not universally Conclusion Hence, the wrong statement is: (C)