If AB = BA = I, what can be said about matrices A and B? a. They are transposes of each other. b. They are inverses of each other. c. They are symmetric. d. They are singular.
Question
If AB = BA = I, what can be said about matrices A and B?
a. They are transposes of each other.
b. They are inverses of each other.
c. They are symmetric.
d. They are singular.
Solution
b. They are inverses of each other.
In matrix algebra, if the product of two matrices (A and B) is the identity matrix (I), then those two matrices are inverses of each other. This is because the definition of an inverse matrix is a matrix which, when multiplied by the original matrix, results in the identity matrix. So, if AB = BA = I, then A and B are inverses of each other.
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