6
QuizMultiple Choice

Matrices and Their Inverses — Quiz

Question 6 • Advanced Algebra: Concepts and Connections

Which value of t makes the two matrices inverses of each other? the 2 by 2 matrix, row 1, column 1, negative 4 column 2, 6 row 2, column 1, 3 column 2, negative 4 the 2 by 2 matrix row 1, 2 3 row 2, 1 point 5 t

Answer
A
2
B
negative 2
C
negative 3
D
3

Explanation

For two matrices to be inverses, their product must be the identity matrix. Multiplying the first matrix by the second, the top-right entry is (−4)(3) + 6t = −12 + 6t, which must equal 0. Solving gives t = 2; the bottom-right entry also becomes 9 − 4(2) = 1, as required. So the correct choice is A, 2.

AI-written and checked against the verified answer.

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