Using the properties of matrices, explain why the following concept is incorrect: Since …
Using the properties of matrices, explain why the following concept is incorrect:
Since $(a+b)(a-b) = a^2 - b^2$, therefore, $(A + B)(A - B) = A^2 - B^2$ also must be true if A and B are matrices.
Answer
Answer
AIWritten by AI - it can contain mistakes.
Matrix multiplication is non-commutative in general ($AB \neq BA$).
Expanding the product of matrix sums gives:
$(A + B)(A - B) = A(A - B) + B(A - B) = A^2 - AB + BA - B^2$.
Since $AB \neq BA$ in general, $-AB + BA \neq 0$, which means $(A + B)(A - B) \neq A^2 - B^2$.
Therefore, the statement is incorrect.
From ISC 2027 Specimen Mathematics Paper 1, question 1(xviii).