The correct option is c. no, because its determinant is zero.
A square matrix is said to be invertible when and only when the determinant is not exactly zero.
A matrix is an rectangular array or table that contains numbers, signs, or expressions structured in rows and columns and is used to depict a mathematical object or a property of one.
The matrix is given as,
[tex]A=\left[\begin{array}{cc}6 & -4 \\-9 & 6\end{array}\right][/tex]
Calculate the determinant of the matrix.
D = ( 6 x 6 ) - ( -9 x -4 )
D = ( 36 - 36 )
D = 0
The matrix's determinant is zero in this case. As a result, the matrix cannot be inverted.
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The complete question is-
Select the correct answer.
justify whether matrix a is invertible.
[tex]A=\left[\begin{array}{cc}6 & -4 \\-9 & 6\end{array}\right][/tex]
a. yes, because its determinant is not equal to zero.
b. yes, because its determinant is greater than zero.
c. no, because its determinant is zero.
d. no, because its determinant is less than zero. e. no, because its determinant is not equal to zero.
