Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Model Papers
0 votes

If $ A = \begin{bmatrix} 2 & 3 \\ 5 & -2 \end{bmatrix} $ write \( A^{-1} \) in terms of A.

Can you answer this question?

1 Answer

0 votes
  • A matrix is said to be singular if $|A|$ =0.
  • A matrix is said to be invertible only if $|A|\neq 0$.
  • $A^{-1}=\frac{1}{|A|}adj \;A$
  • The adjoint of a square matrix A=[$a_{ij}]_{n\times n}$ is defined as the transpose of the matrix$ [A_{ij}]n\times n$
  • where $A_{ij}$ is the cofactor of the element $[a_{ij}].$
Step 1:
$A=\begin{bmatrix}2 &3\\5&-2\end{bmatrix}$
$\mid A\mid=-4-15=-19$
$\neq 0$
Hence inverse exists
Step 2:
Adj A=$\begin{bmatrix}-2 &5\\3&2\end{bmatrix}$
$A^{-1}=\large\frac{1}{\mid A\mid}$$(adj A)$
$\qquad=\large\frac{1}{-19}$$\begin{bmatrix}-2&5\\3 & 2\end{bmatrix}$
answered Nov 12, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App