ID: Class: 12Subject: MathTopic: Matrices and DeterminantsType: McqYear: 2025
Question:
If A and B are square matrices of order m such that \(A^{2}-B^{2}=(A-B)(A+B),\) then which of the following is always correct?
A. \(A=B\)
B. \(AB=BA\)
C. \(A=0\) or \(B=0\)
D. \(A=I\) or \(B=I\)
Official Solution
Correct Answer: \(AB=BA\)
Explanation:
The identity $A^2 - B^2 = (A - B)(A + B)$ holds for square matrices $A$ and $B$ only if they commute, i.e., $AB = BA$.
This is because matrix multiplication is not generally commutative.
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