Find the value of (lamda) if (lamda)[tex]A^{-1}[/tex] =A and A=[tex]\left[\begin{array}{ccc}2&3\\5&-2\\\end{array}\right][/tex]
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Find the value of (lamda) if (lamda)[tex]A^{-1}[/tex] =A and A=[tex]\left[\begin{array}{ccc}2&3\\5&-2\\\end{array}\right][/tex]
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Step-by-step explanation:
AA
−1
=I
A
−1
A=I
A matrix that has a multiplicative inverse is called an invertible matrix. Only a square matrix may have a multiplicative inverse, as the reversibility, \displaystyle A{A}^{-1}={A}^{-1}A=IAA
−1
=A
−1
A=I, is a requirement. Not all square matrices have an inverse, but if \displaystyle AA is invertible, then \displaystyle {A}^{-1}A
−1
is unique. We will look at two methods for finding the inverse of a \displaystyle 2\text{}\times \text{}22×2 matrix and a third method that can be used on both \displaystyle 2\text{}\times \text{}22×2 and \displaystyle 3\text{}\times \text{}33×3 matrices.
Hope its help.