Question

Determine whether each pair of matrices are inverses.12.

$\mathbf{A}\mathbf{=}\left[\begin{array}{cc}6& 2\\ 5& 2\end{array}\right]$

$\mathbf{B}\mathbf{=}\left[\begin{array}{cc}1& 1\\ \mathbf{-}\frac{5}{2}& -3\end{array}\right]$

Short answer

The given matrices are not inverse of each other.

Step-by-step solution

­- Definition of inverse of matrix.

A square matrixB is said to be an inverse of the square matrixA if$\mathbf{AB}\mathbf{=}\mathbf{BA}\mathbf{=}\mathbf{I}$whereI is an identity matrix of the same order as that of matrix Aor B.

­- Find the product of the given matrices.A⋅B=[6252]⋅[11−52−3]=[(6)(1)+(2)(−52)(6)(1)+(2)(−3)(5)(1)+(2)(−52)(5)(1)+(2)(−3)]=[6+(−5)6+(−6)5+(−5)5−6]=[6−56−65−55−6]=[100−1]As the product of the given matrices is not equal to the identity matrix, therefore the given matrices are not inverse of each other.

The product of the given matrices is:

­- Write the conclusion. 

The given matrices are not inverse of each other.