Determine whether the function involving the n × n matrix A is a linear transformation.T: Mn,n → Mn,n, T(A) = A−1
Question
Solution 1
To determine whether a function is a linear transformation, it must satisfy two properties:
- Additivity: T(A + B) = T(A) + T(B)
- Scalar multiplication: T(cA) = cT(A)
where A and B are matrices, and c is a scalar.
Let's check these properties for the function T(A) = A−1.
- Additivity:
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