Let A,B be transformations (for example, let A correspond to the reflection of a point across the x-axis, and B the rotation of a point counterclockwise around the origin). Explain why the inverse of AB is NOT A−1B−1. Your answer must refer to interpreting A,B as transformations. B)Prove: If a,b,∈R and P is a m×n matrix, then aP+bP=(a+b)P

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Given a matrix M, a left-inverse is a matrix L where LM=I, the identity matrix of the appropriate size; and a right-inverse is a matrix R where MR=I, the identity matrix of the appropriate size.

Let A,B be transformations (for example, let A correspond to the reflection of a point across the x-axis, and B the rotation of a point counterclockwise around the origin).

Explain why the inverse of AB is NOT A−1B−1. Your answer must refer to interpreting A,B as transformations.
 
B)Prove: If a,b,∈R and P is a m×n matrix, then aP+bP=(a+b)P
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