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Type: Multiple-Choice
Category: Matrices
Level: Grade 12
Standards: HSN-VM.C.10
Author: nsharp1
Created: 5 years ago

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Grade 12 Matrices CCSS: HSN-VM.C.10

James needs to show that for matrix

$A = [[5,-2,1],[3,3,2],[-6,3,-1]]$ , there is no matrix

$B, B!=I$ , such that

$AB = I$ , where

$I$ is the 3-by-3 identity matrix. How can he do this?

Try at least 3 matrices, and if none of them multiplied by $A$ equal the identity matrix, then it is not possible.
Find the inverse of $A$ , and then show that since this matrix is unique, there cannot exist another matrix $B$ such that $AB = I$ .
Subtract by the additive inverse on both sides, and then factor the left hand side of the equation. This implies that if $B=I$ the equation equals the zero matrix, which it can't.
Show that the determinant of $A$ is zero, which means that it does not have a multiplicative inverse.