# if A is a square matrix of order 3 such that modulus A = 5 then write the value of A (adj A)

In the given question, we are given a square matrix of order 3 such that $\left|A\right|=5$. We need to find $\left|A.adjA\right|$.

Here, use the formula ${A}^{-1}=\frac{adjA}{\left|A\right|}$. So,
${A}^{-1}.\left|A\right|=adjA\phantom{\rule{0ex}{0ex}}$

Next, multiply left hand side and right hand side by A, we get
$A.{A}^{-1}.\left|A\right|=A.adjA\phantom{\rule{0ex}{0ex}}$

No, use the fact that $A.{A}^{-1}={I}_{3}$ where I3 is the identity matrix of order 3. So,
$\left|A\right|.{I}_{3}=A.adjA\phantom{\rule{0ex}{0ex}}\left|\left|A\right|.{I}_{3}\right|=\left|A.adjA\right|\phantom{\rule{0ex}{0ex}}{\left|A\right|}^{3}=\left|A.adjA\right|\phantom{\rule{0ex}{0ex}}{5}^{3}=\left|A.adjA\right|\phantom{\rule{0ex}{0ex}}\left|A.adjA\right|=125$

Therefore, $\left|\mathbf{A}\mathbf{.}\mathbf{a}\mathbf{d}\mathbf{j}\mathbf{A}\right|\mathbf{=}\mathbf{125}$

• 1

25

• 0

how do we solve it?

• -1
What are you looking for?