GATE ME 2014 Set 4 — Question 11
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Engineering Mathematics → Linear Algebra → Matrix Algebra & Operations
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Question
Which one of the following equations is a correct identity for arbitrary real matrices and ?
Correct answer
(D) (P + Q)² = P² + PQ + QP + Q²
Solution
Matrix multiplication is distributive over addition, so . Option (A) is incorrect because it states instead of . Matrix multiplication is generally not commutative (), so . Thus, option (B) is incorrect. The determinant of a sum is not equal to the sum of determinants in general, so option (C) is incorrect. Finally, , which is always true for any matrices. Thus, option (D) is the correct identity.
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