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3. Consider the laws of exponents A" A = A"+s and (A")* = A"8. (a) Show that if A is any square matrix, then these laws are valid for all non negative integer values of r and s. (b) Show that if A is invertible, then these laws hold for all negative integer values of r and s.

3. Consider the laws of exponents A" A = A"+s and (A")* = A"8. (a) Show that if A is any square matrix, then these laws are valid for all non negative integer values of r and s. (b) Show that if A is invertible, then these laws hold for all negative integer values of r and s.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Consider the laws of exponents A" A$ = A"+8 and (A")$ = A"s. (a) Show that if A is any square matrix, then these laws are valid for all non negative integer values of r and s. (b) Show that if A is invertible, then these laws hold for all negative integer values of r and s.
Transcribed Image Text:3. Consider the laws of exponents A" A$ = A"+8 and (A")$ = A"s. (a) Show that if A is any square matrix, then these laws are valid for all non negative integer values of r and s. (b) Show that if A is invertible, then these laws hold for all negative integer values of r and s.
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