Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Suppose that A is an nxn invertible matrix. Prove the following statements: 

(a) If there exists an nxn matrix D such that AD=I_n then D=A^-1.

(b) If B and C are matrices such that A(B-C)=0 (where 0 is a zero matrix of appropriate size), then B=C. 

Hint: Both of these are simplier to prove using matrix algebra rather than the definition of matrix multiplication. 

I_n is the identity matrix and A^-1 is A inverse matrix.  

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