GATE CS 2022 Set 1 — Question 20
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Engineering Mathematics → Linear Algebra → Matrices & Determinants
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Question
Consider the following two statements with respect to the matrices and .Statement 1:
Statement 2: .where represents the trace of a matrix. Which one of the following holds?
Statement 2: .where represents the trace of a matrix. Which one of the following holds?
Correct answer
(C) Both Statement 1 and Statement 2 are correct.
Solution
The trace of a product of two matrices and satisfies provided that both products and are square matrices.
- In Statement 1, is and is . Thus is and is . Both are square, so is a standard identity.
- In Statement 2, and are both . Thus and are both . Both are square, so is also a standard identity.
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