If $\mathrm{A}^{-1}=\left[\begin{array}{ccc}3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ccc}1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1\end{array}\right]$, find $(\mathrm{AB})$

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Algebra

NCERT Class 12 Part 1 - Math

Chapter 4

Determinants

Section 7

Applications of Determinants and Matrices

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Video Transcript

We have fallen # seven. In this we have been provided inverse metrics which is three minus 15, 3 -15 5, then minus 16 minus two, Then one miles 5 and two and be equal to 1: -2. And Mine's 1, 3, 0 and then 0 -2 and one. So we need to find baby A into B. It's invest we know that A B. Universe equal to be inverse into universe. Universe is already given. That's right. One universe is already given. So we have to find being with for that uh we have formula B. University people too. One by determinant of B into a joint of be. So we have to first find the determinant of B. And agenda. B is the transpose of the conflict metrics Or be let us determine beat Uh determinant. So this will be one into 3 0. And at first we were operating -2 -1 0. Bless minus two To zero. So this is three plus two minus four. Richard, Lynn not equal to zero. So in verse is possible. So let us start finding the co victors. First call affected. We should be writing even when be fun fun because this is the co factor of their matters be be 11 So it is like Uh to find the co director of this because this is 11 1st row first column element. So it is just plus minus plus minus plus minus bless minus bless. And We will be leaving this and determinant, 3 0 -2 one. So get plus sign, it is 30 minus 21 So conflicted will be three minus zero, simply three to be 12 will be with a negative sign -1001, this is one B 13 bit positive same -1, -2. This will be too and B to win with negative sign with negative sign it will be mhm two minus two minus 21 That is okay to one to minus two minus two. Fun this will be too 2 -4 years, took B- 22 with positive sign and determinant will pay one minus two 01 That is 1 0 which is one B 23 with a negative sign uh -2. So it will be one two 0 -2. This is two B 31 Will be equal to with plus sign to -2 3036. B 32 the negative sign and 1 -2 -1 and zero. So this will be too B three three with positive sign 1 to -13 that is five. So let us write a joint of B. It will be transport transport of the court convicted metrics. So let us lie right, coffee. Automatic 1st 312 212625. And its transport transform means will be changing ruled by columns three. First struggle become first column, second row will become second column, third row will become 3rd column. So this is the giant metric. No, the universe will be equal to one by one. One means determinant and then one x 1 and then a joint a joint of B. So if you multiply with one, a joint of people be simply a joint of be so being versus 312212 6 to 5. Now we have to find maybe in verse A B inverse which is B inverse into the universe. So be in verses uh 312 2 1, 2 and 6- five. And Aid versus 3 -1, 1 which has been given minus 15, six minus five than five -2 and two. So we have to find its multiplication and to get the results. Yeah. So multiplication will be rule with column. So we'll be having 3, 3 9 minus 30 33 into 39 to minus 15 minus 36 to 5 30. Similarly, three to minus one minus three Plus 12, 9, 12, 3 -10 plus 12, 3 -15 plus 10 minus one plus six minus four, 1 -5 Plus four, 6 -30 day plus 25- to plus 12 -10 to my understand. And bless then, So if you add it up it will be nine Yeah minus three, five -2, 102 So this is the required value of a B. Universe. Thank you.

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