If ( A = begin{bmatrix} 2 & 3 4 & 5 end{bmatrix} ), find the matrix ( B ) such that ( AB = I ) where ( I ) is the identity matrix.

Question

If ( A = begin{bmatrix} 2 & 3  4 & 5 end{bmatrix} ), find the matrix ( B ) such that ( AB = I ) where ( I ) is the identity matrix.

Accepted Answer

Step:1 ：Step 1: Start with the equation ( AB = I ).Step:2 ：Step 2: To solve for ( B ), we need to find the inverse of ( A ) because ( A^{-1}A = I ). So, ( B = A^{-1} ).Step:3 ：Step 3: The formula for the inverse of a 2x2 matrix ( A = begin{bmatrix} a & b  c & d end{bmatrix} ) is ( A^{-1} = frac{1}{ad-bc} begin{bmatrix} d & -b  -c & a end{bmatrix} ).Step:4 ：Step 4: Substituting the given values, we get ( A^{-1} = frac{1}{2*5 - 3*4} begin{bmatrix} 5 & -3  -4 & 2 end{bmatrix} = frac{1}{-2} begin{bmatrix} 5 & -3  -4 & 2 end{bmatrix} = begin{bmatrix} -5/2 & 3/2  2 & -1 end{bmatrix} ).

Answer

Step: 1 ：Step 1: Start with the equation ( AB = I ).Step: 2 ：Step 2: To solve for ( B ), we need to find the inverse of ( A ) because ( A^{-1}A = I ). So, ( B = A^{-1} ).Step: 3 ：Step 3: The formula for the inverse of a 2x2 matrix ( A = begin{bmatrix} a & b  c & d end{bmatrix} ) is ( A^{-1} = frac{1}{ad-bc} begin{bmatrix} d & -b  -c & a end{bmatrix} ).Step: 4 ：Step 4: Substituting the given values, we get ( A^{-1} = frac{1}{2*5 - 3*4} begin{bmatrix} 5 & -3  -4 & 2 end{bmatrix} = frac{1}{-2} begin{bmatrix} 5 & -3  -4 & 2 end{bmatrix} = begin{bmatrix} -5/2 & 3/2  2 & -1 end{bmatrix} ).

If $A = [\begin{matrix} 2 & 3 \\ 4 & 5 \end{matrix}]$ , find the matrix $B$ such that $A B = I$ where $I$ is the identity matrix.

Answer

Popular Problems

If A=[2345], find the matrix B such that AB=I where I is the identity matrix.

Answer

Popular Problems

If $A = [\begin{matrix} 2 & 3 \\ 4 & 5 \end{matrix}]$ , find the matrix $B$ such that $A B = I$ where $I$ is the identity matrix.