If A and B are invertible matrices of the sam | vedclass

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Question

(A) Step $1$: The fundamental property of the adjoint of a matrix $A$ is $A(	ext{adj } A) = (	ext{adj } A)A = |A|I$, where $|A|$ is the determinant

Vedclass · Accepted Answer

$A(	ext{adj } A) = (	ext{adj } A)A = AI$

Vedclass · Answer

(A) Step $1$: The fundamental property of the adjoint of a matrix $A$ is $A(	ext{adj } A) = (	ext{adj } A)A = |A|I$, where $|A|$ is the determinant of $A$ and $I$ is the identity matrix.Step $2$: Option $(A)$ states $A(	ext{adj } A) = (	ext{adj } A)A = AI$. This is incorrect because it omits the determinant factor $|A|$.Step $3$: Option $(B)$ is the correct identity. Option $(C)$ is the standard reversal law for the inverse of a product of matrices. Option $(D)$ is the condition for a matrix to be invertible.Step $4$: Therefore, the incorrect statement is $(A)$.

If $A$ and $B$ are invertible matrices of the same order, then which of the following is not correct?

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