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If ๐ด = [โˆ’2 43 โˆ’1] ๐‘Ž๐‘›๐‘‘ ๐ต = [1 34 โˆ’1], then verify that either B is a multiplicative inverse ofA or not?

Question

If ๐ด = [โˆ’2 43 โˆ’1] ๐‘Ž๐‘›๐‘‘ ๐ต = [1 34 โˆ’1], then verify that either B is a multiplicative inverse ofA or not?

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Solution

To verify if B is a multiplicative inverse of A, we need to multiply matrix A by matrix B. If the result is an identity matrix, then B is a multiplicative inverse of A.

However, in this case, A and B are not square matrices, they are 1x3 matrices. The concept of multiplicative inverse is not defined for non-square matrices.

Therefore, we cannot verify if B is a multiplicative inverse of A because the concept does not apply to these matrices.

This problem has been solved

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check that B is the correct inverse using R

๐‘†๐‘ข๐‘๐‘๐‘œ๐‘ ๐‘’ย ๐‘กโ„Ž๐‘Ž๐‘กย ๐‘กโ„Ž๐‘’ย ๐‘โ„Ž๐‘Ž๐‘Ÿ๐‘Ž๐‘๐‘ก๐‘’๐‘Ÿ๐‘–๐‘ ๐‘ก๐‘–๐‘ย ๐‘๐‘œ๐‘™๐‘ฆ๐‘›๐‘œ๐‘š๐‘–๐‘Ž๐‘™ย ๐‘œ๐‘“ย ๐‘ ๐‘œ๐‘š๐‘’ย ๐‘š๐‘Ž๐‘ก๐‘Ÿ๐‘–๐‘ฅย ๐ดย ๐‘–๐‘ ย ๐‘“๐‘œ๐‘ข๐‘›๐‘‘ย ๐‘ก๐‘œย ๐‘๐‘’ย ๐‘(๐œ†)ย =ย (๐œ†ย -ย 1)๐œ†ย -32ย ย ๐œ†ย -43ย ย .ย ๐‘Šโ„Ž๐‘Ž๐‘กย ๐‘–๐‘ ย ๐‘กโ„Ž๐‘’ย ๐‘ ๐‘–๐‘ง๐‘’ย ๐‘œ๐‘“ย ๐ด?

Are 8 7โ€“6 3 and 12โ€“92โ€“5252 multiplicative inverses?

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