Mathematics · Linear Algebra
Let M2(ℝ) be the vector space of all 2×2 matrices over ℝ. Consider the linear transformation T: M2(ℝ) → M2(ℝ) defined by T(X) = AXB, where: A = [ 1 -2 ; 1 4 ] and B = [ 6 5 ; -2 -1 ]. If P is the matrix representation of T with respect to the standard basis of M2(ℝ), then which of the following statements is TRUE?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The nullity of (P - 2I4) is 0, where I4 is the 4×4 identity matrix
- 2The rank of (P2 - 4I4) is 4, where I4 is the 4×4 identity matrix
- 3The trace of P is 25✓
- 4P is an invertible matrix
Correct answer
The trace of P is 25
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