Matrices and Their Inverses — Quiz

Question 8 • Advanced Algebra: Concepts and Connections

Which pair of matrices are inverses of each other?

Answer

the 2 by 2 matrix row 1, 2 3 row 2, 6 8 the 2 by 2 matrix, row 1, column 1, negative 1 column 2, 3 halves row 2, column 1, 3 column 2, negative 4

the 2 by 2 matrix row 1, 2 3 row 2, 6 8 the 2 by 2 matrix, row 1, column 1, 4 column 2, negative 3 halves row 2, column 1, negative 3 column 2, 1

the 2 by 2 matrix row 1, 2 3 row 2, 6 8 the 2 by 2 matrix, row 1, column 1, 1 column 2, negative 3 halves row 2, column 1, negative 3 column 2, 4

the 2 by 2 matrix row 1, 2 3 row 2, 6 8 the 2 by 2 matrix, row 1, column 1, negative 4 column 2, 3 halves row 2, column 1, 3 column 2, negative 1

Explanation

For a 2 by 2 matrix [[a, b], [c, d]], the inverse is 1/(ad − bc) times [[d, −b], [−c, a]]. The determinant of [[2, 3], [6, 8]] is 2·8 − 3·6 = −2, so its inverse is [[−4, 3/2], [3, −1]]. This is the matrix in choice B.

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