Let , A is a non-singular idempotent matrix of order 3× 3 and B is an involuntary matrix of same order. If textdet(A)≠ det (B) , then textdet(A- 5 B- 2)=

Question

Let , A is a non-singular idempotent matrix of order 3× 3 and B is an involuntary matrix of same order. If textdet(A)≠ det (B) , then textdet(A- 5 B- 2)= (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

textdet(A)=1, textdet (B)=-1 ⇒ textdet (A- 1)=1, textdet ⁡ (B- 1)=-1

Q. Let , $A$ is a non-singular idempotent matrix of order $3 \times 3$ and $B$ is an involuntary matrix of same order. If $det (A) \neq = d e t (B)$ , then $det (A^{- 5} B^{- 2}) =$

$det (A) = 1, det (B) = - 1$
$\Rightarrow det (A^{- 1}) = 1, det (B^{- 1}) = - 1$

Q. Let , A is a non-singular idempotent matrix of order 3×3 and B is an involuntary matrix of same order. If det(A)=det(B) , then det(A−5B−2)=

det(A)=1,det(B)=−1 ⇒det(A−1)=1,det⁡(B−1)=−1

Q. Let , $A$ is a non-singular idempotent matrix of order $3 \times 3$ and $B$ is an involuntary matrix of same order. If $det (A) \neq = d e t (B)$ , then $det (A^{- 5} B^{- 2}) =$

$det (A) = 1, det (B) = - 1$
$\Rightarrow det (A^{- 1}) = 1, det (B^{- 1}) = - 1$