## Suppose (B – C)D = 0, where B and C are m * n matrices and D is invertible.

Advanced MathSuppose (B – C)D = 0, where B and C are m * n matrices and D is invertible. 2 years ago
Suppose (B - C)D = 0, where B and C are m * n matrices and D is invertible. Show that B = C

Step 1

Since D is invertible then D^(-1)exist and DD^(-1)=I_n. Here B and C are m * n matrices such that

(B-C)D=0

-> (B-C)D * D^(-1)=0 * D^(-1)

-> (B-C)(D-D^(-1))=0

-> B-C=0

-> B=C

Step 1

We know that (B-C)D=0

Since D it invertible, D has an inverce D^(-1)

We multiply both sides of (B-C)D=0 by D^(-1) on the right side:

(B-C)D * D^(-1)=0 * D^(-1)

Note that 0D^(-1)=I_n, and 0D^(-1)}=0

So we are left with B-C=0, which rearranges to B=C

Step 1

( B - C )D = 0 where B and C are m * n matrix and D is invertible.

Then, we have to prove that B = C.

Step 2

Since, D is invertable so D^(-1) exist.

Now, from the given equation (B-C)D=0

(B-C)DD^(-1)=OD^(-1)ZSK

(B-C)I=O

B-C=O

Or, B=C

Thus, we obtained our desired result.

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